Background radiation suppression in MUON detector

Abstract

A method filters noise from measured data obtained by a muon detector. The method comprises: obtaining a measured distribution of path-length-adjusted energy data for a plurality of detection events associated with the measured data: providing a first baseline distribution of deposition energy per unit path length obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; providing a second baseline distribution of deposition energy per path length obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; fitting the measured distribution to the first and second baseline distributions wherein fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and filtering the measured data obtained by the detector based at least on the determined distribution fitting parameters to thereby obtain noise-filtered measured data.

Description

BACKGROUND RADIATION SUPPRESSION IN MUON DETECTORCross-Reference to Related Applications

[0001] This application claims priority from, and for the purposes of the United States of America the benefit under 35 USC 119 in connection with, United States application No. 63 / 761,143 filed 20 February 2025 and United States application No.63 / 796,745 filed 29 April 2025, which are hereby incorporated herein by reference.Field

[0002] The technology disclosed herein relates to tracking cosmic ray muons with a muon detector deployed underground (e.g. in a borehole), and in particular to filtering noise (e.g. generated by other particles) in trajectory data collected by the muon detector.Background

[0003] Muon detectors may be deployed underground (e.g. in boreholes) to track cosmic ray muons and in turn generate muon trajectory data for modelling subsurface environment (e.g. modelling subsurface densities using tomographic techniques). Valuable intelligence about region(s) of interest may be derived from such models.

[0004] There are various types of muon detectors suitable for deployment underground. For example, some muon detectors comprise scintillating fibers and / or scintillating bars for sensing the presence of muons.

[0005] FIG. 1 A is a schematic partial perspective view of a cross-section of a prior art muon detector 10A which is generally cylindrically shaped for deployment in a borehole. Muon detector 10A comprises a first plurality of scintillator fibers 20 wound in clockwise along a longitudinal length of muon detector 10A (the longitudinal direction shown schematically by double-head arrow 18 and being parallel with the cylindrical axis of detector 10A) to form a first helical bundle 52 of scintillator fibers 20 and a second plurality of scintillator fibers 20 wound counterclockwise along the longitudinal length of muon detector 10A to form a second helical bundle 54 of scintillator fibers 20. First and second helical bundles 52 and 54 may be mounted on a hollow cylindrical (annular cylinder) mandrel (not expressly shown in FIG. 1 A) to form an outer cylinder 56 shaped to define a bore 58.

[0006] Muon detector 10A comprises a plurality of scintillator bars 24 extending in longitudinal direction 18 and arranged radially symmetrically about a centrallongitudinal axis 14 of muon detector 10A to form an inner cylinder 60. In FIG. 1 A, there are two sizes of scintillator bars 24, both of which have a triangular cross section. Scintillator bars 24 having smaller cross section are on an inner side 66 of inner cylinder 60 and scintillator bars 24 having larger cross section are on an outer side 70 of inner cylinder 60. Muon detector 10A may comprise photodetectors (not shown) respectively operatively coupled to one or both ends of each of scintillator fibers 20 and each of scintillator bars 24 for detecting scintillation light.

[0007] In operation, muon detector 10A may be deployed in a borehole, where data generated by muon detector 10A may be used by suitably configured processor(s) to determine the entry points of muon particles into detector 10A and the exit points of muon particles out of detector 10A based on scintillation light generated from scintillator fibers 20 in both first helical bundle 52 and second helical bundle 54 and scintillation light generated from scintillator bars 24 in inner cylinder 60.

[0008] FIG. 1 B is a schematic partial perspective view of a cross-section of another prior art muon detector 10B. Muon detector 10B is similar to muon detector 10A except that muon detector 10B has only one helical bundle 52 of scintillator fibers 20 wound along the longitudinal length of muon detector 10B and mounted on a mandrel 53. In operation, muon detector 10B may be applied to determine the entry points of muon particles into muon detector 10B and the exit points of muon particles out of muon detector 10B based on scintillation light generated from scintillator fibers 20 in helical bundle 52 and from scintillator bars 24 in inner cylinder 60, and timing information (e.g. a global time stamp) about the detection of scintillation at the respective photodetectors (not shown) operatively coupled to the ends of scintillator fibers.

[0009] When charged particles pass through muon detectors, such as muon detectors 10A and 10B, that utilize sub-detector elements (e.g. scintillator fibers 20, scintillator bars 24, etc.) sensitive to charged particles, the passing particles deposit some of their energy in the sub-detector elements. The energy deposition is a stochastic process, and both the mean deposited energy per unit path length through material, and the probability distribution of deposited energy, can be predicted from physical theory. Regardless, the deposited energy in turn causes the traversed subdetector elements to generate a detectable output (e.g. scintillation light and / or ionization of gas atoms) for detection by suitable sensors to induce corresponding electronic signals (e.g. photodetectors, electrical current sensors and / or the like).When at least two discrete spatiotemporal points (x,y,z,t), each corresponding to some combination of distinct sub-detector element outputs, can be identified in a given time window, a trajectory can be estimated by generating a best fit line through the spatial coordinates (x,y,z) of the discrete spatiotemporal points. The trajectory may then be included in trajectory data and may be recognized as a detection event (also, referred to, on occasion, as a track detection or a track detection event).

[0010] One challenge with deploying muon detectors comprising sub-detector elements sensitive to charged particles underground (e.g. in boreholes), where muon flux is less pervasive than at the surface of the earth, is that other (non-muon) charged particles may pass through the detector and may also deposit their energy in the sub-detector elements, thereby mimicking energy deposition of muon particles.

[0011] For example, in a typical underground environment, there may exist a plurality of naturally occurring beta particle sources, e.g., radioactive isotopes found in rocks, soil, and groundwater. These naturally occurring beta particle sources continuously emit beta particles, which may impinge on muon detectors deployed underground. As the beta particles pass into the muon detectors, the beta particles deposit their energy in the muon detector sub-detector elements. The energy deposited by beta particles may mimic energy deposition by a muon particle, thereby creating noise in the trajectory data and reducing the intelligibility in the muon trajectory data (e.g. the ability to discern muon detection events from detection events associated with other particles).

[0012] FIG. 2A is a histogram chart 90A showing the count of detection events corresponding to a range of zenith angle values (0) of reconstructed trajectories generated by a muon detector (e.g. one of muon detectors 10A, 10B described above, although that is not necessary) in a controlled environment. The controlled environment of the histogram shown in FIG. 2A has a relatively much more significant muon flux compared to the flux of other particles. FIG. 2B is a histogram chart 90B showing the count of detection events corresponding to a range of zenith angle values of reconstructed trajectories generated by the same muon detector when deployed on-site in an environment with significant beta radiation. The zenith angle values 0 in FIGs. 2A and 2B are expressed in radians and have a range of ~ 0 rad < © < 1.75 rad.

[0013] As can be seen in FIG. 2A, histogram chart 90A shows a gradual increase in the count of detection events from lower 0 values to higher 0 values with the mode(i.e. peak) of the distribution located at about 0=0.9 rad, with a significant count of detection events recorded between about 0.7 rad < 0 < 1.2 rad. In contrast, in FIG.2B, histogram chart 90B has a mode (i.e. peak) of the distribution located at about 0=0.4 rad with a significant count of detection events recorded between about 0.05 rad < 0 < 0.5 rad. Moreover, when comparing distributions 90A (FIG. 2A) and 90B (FIG. 2B), distribution 90B exhibits a right skew with a relatively long tail in the range of about 0.7 rad < 0 < 1.75 rad. The skew is not exhibited in the FIG. 2A histogram chart 90A.

[0014] At least one cause contributing to the unexpected cluster of detection events at smaller 0 values exhibited in the on-site data as shown in FIG. 2B histogram 90B is the non-zero probability of the muon detector detecting naturally occurring beta particles from known underground beta particle sources. The addition of the beta radiation contribution obscures the true muon track angle distribution, and thus prevents efficient use of muon attenuation inferences to measure geological properties.

[0015] Muon particles from cosmic rays typically have mean kinetic energy larger than 1000 MeV and are highly penetrative, while naturally occurring beta particles generally have an upper kinetic energy limit of around 5 MeV. Given the difference in mean kinetic energy of cosmic ray muon particles and naturally occurring beta particles, it is conceivable to reduce the noise due to beta particle flux by shielding the detector with absorptive materials to absorb the energy of passing particles. For example, shielding may be selected to have an absorptive strength to prevent a significant portion of the naturally occurring beta particles from penetrating the detector while still allowing sufficient cosmic ray muon particles to pass through. However, there are at least two challenges to shielding a detector with absorptive materials underground. First, underground muon detectors typically need to be provided in small form-factors since it is desirable, for example, for such muon detectors to be deployed in boreholes or in confined spaces in underground mines. Therefore, there is often insufficient space to provide adequate shielding to reduce the beta particle flux through the detector to achieve a desirable signal-to-noise ratio of muon particle tracks to beta particle tracks. Second, in underground environments, the natural muon particle flux is relatively low since the cosmic ray muon particles are typically strongly attenuated by the overburden (earth above the detector) when they reach the detector, whereas many beta particles are generated from rocks that arerelatively proximal to the detector. Therefore, a shielding adequate for blocking the beta particles may require so much material to attain the desired level of signal-to-noise ratio, that the detector (together with shielding) becomes too heavy to reasonably maneuver and deploy. Moreover, the signal-to-noise ratio of muon particle tracks to beta particle tracks generally worsens with increasing depth, because the muon flux weakens with depth but the beta particle rate may remain relatively constant or even increase with depth depending on the concentration of beta-emitting isotopes in the surrounding rock mass. As a result, the degree of shielding required to achieve an acceptable signal-to-noise ratio varies significantly with deployment depth and local geology, making passive shielding alone an impractical solution for reliably distinguishing muon particle tracks from beta particle noise across diverse underground environments.

[0016] Some detector designs may be able to distinguish between beta and muon particle signals. One example design is a Cherenkov radiation detector. A Cherenkov radiation detector relies on the Cherenkov Effect, where charged particles travelling through a medium at a speed greater than the speed of light in the medium emit a faint blue or ultraviolet light. The emitted light is referred to as Cherenkov radiation. The characteristic light cone from emitted Cherenkov radiation is related to the relativistic gamma factor. The relativistic gamma factor of naturally occurring beta particles (with energies typically < 5MeV) and the relativistic gamma factor of muon particles are appreciably different, thus permitting beta particles to be distinguished from muon particles. However, it is not practical to deploy a Cherenkov radiation detector underground (e.g. in narrow boreholes) due to at least the space constraint underground.

[0017] One challenge related to discriminating beta particle interactions from muon particle interactions with a muon detector relates to the variation in possible trajectories of particles through the muon detector, and in particular path length of the trajectories. A particle that traverses the muon detector in a trajectory with a relatively long path length can deposit more of its energy into the detector compared to a particle with similar or same energy profile that traverses the muon detector in a trajectory with a relatively short path length. As a result, simply attempting to discriminate between muons and beta particles based on total deposited energy will preferentially select muon particles based on their path length through the detector and may undesirably reject some muons with short path lengths through the detector.This undesirable rejection of short-path-length muons may in turn preclude the ability to measure the directional muon flux from certain directions with high precision, as those muon particle tracks will be preferentially rejected from the dataset and the precise efficiency of such rejection will need to be known to deduce what is the true underlying muon flux in the preferentially excluded directions. Further, detailed simulations and measurements have shown that in environments where the beta particle rate exceeds the muon rate by many orders of magnitude, applying total energy deposition as a discrimination criterion fails to eliminate all of the beta particle noise. At least some of beta particles, through quantum fluctuations in their energy loss behavior, deposit a total energy similar to that of muon particles and survive the total energy discrimination criterion. These residual beta particles still introduce problematic noise in the trajectory data.

[0018] Another challenge related to discriminating beta particle interactions from muon particle interactions with a muon detector relates to the attenuation of the detectable output generated by sub-detector elements. At least some muon detectors for deployment underground (like muon detectors 10A, 10B described above) are designed to have a longitudinal extension (and relatively small area in a cross-section of their longitudinal dimension) for ease of deployment into a borehole, for example. In some such detectors, the sub-detector elements (e.g. scintillator fibers 20, scintillator bars 24) may often extend in longitudinal direction 12 from one longitudinal end of the detector to the other longitudinal end of the detector, with photodetector elements located proximate to one or both longitudinal ends of the scintillator fibers 20 and scintillator bars 24. A traversing particle may intersect a sub-detector element at any location along the longitudinal extension of the muon detector. Some of the signal energy generated by a particle intersecting with a sub-detector element (e.g. scintillator fibers 20 and scintillator bars 24) may be lost in the sub-detector element as the signal travels from the particle intersection location to the photodetector(s) or other sensor(s) at the longitudinal end(s) of the muon detector, resulting in attenuation of the signal energy. The locations where particles impinge on a muon detector may therefore impact the photodetector output. As a result, simply attempting to discriminate between muons and beta particulars based on total deposited energy will preferentially select muon particles based on their impact position with the detector and may undesirably reject some muons which impact the detector at locations that are relatively distal from the ends of the detector. Thisundesirable rejection of distal-from-the-detector-ends muons may in turn preclude the ability to measure the directional muon flux from certain directions with high precision, as those muon particle tracks will be preferentially rejected from the dataset, and the precise efficiency of such rejection will need to be known to deduce what is the true underlying muon flux in the preferentially excluded directions.

[0019] Another challenge related to discriminating beta particle interactions from muon particle interactions with a muon detector relates to the fact that there are scenarios where multiple beta particles may enter the detector at different positions such that their collective interactions with the muon detector mimic the total energy deposition of a single muon traversing the muon detector. Consequently, simply attempting to discriminate between muons and beta particles based on total deposited energy will likely fail to filter such “multi-beta hits” that mimic the total energy deposition of a single muon.

[0020] Based on the foregoing, there is a general desire for systems and methods for filtering noise in trajectory data generated by muon detectors. There is a general desire for systems and methods for differentiating and / or filtering energy depositions by non-muon particles from energy depositions by muon particles in muon detectors, particularly, but without limitation, for muon detectors used in boreholes or otherwise deployed underground.Summary

[0021] One aspect of the invention provides a method for filtering noise from measured data obtained by a muon detector. The method comprises: obtaining a measured distribution of path-length-adjusted energy data for a plurality of detection events associated with the measured data, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the path-length-adjusted energy data is representative of energy deposited by the corresponding particle per unit path length in the detector; fitting the measured distribution to first and second baseline distributions of deposition energy per unit path length wherein: the first baseline distribution of deposition energy per unit path length is obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; the second baseline distribution of deposition energy per path length is obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributionscomprises determining a plurality of distribution fitting parameters; and, filtering the measured data obtained by the detector based at least on the determined distribution fitting parameters to thereby obtain noise-filtered measured data.

[0022] Another aspect of the invention provides an apparatus for filtering measured data obtained by a muon detector where the measure data comprises a plurality of detection events, each detection event associated with interaction of a corresponding charged particle with the muon detector. The apparatus comprises: an energy sensing system for determining, for each detection event, a measured energy deposited by the corresponding particle in the muon detector; a processor connected to the energy sensing system to receive, for each detection event, the measured energy, the processor configured to: determine a measured distribution of path-length-adjusted energy data for the plurality of detection events, wherein, for each detection event, the path-length-adjusted energy data is representative of energy deposited by the corresponding particle per unit path length in the detector; fit the measured distribution to first and second baseline distributions of deposition energy per unit path length wherein: the first baseline distribution of deposition energy per unit path length is obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; the second baseline distribution of deposition energy per path length is obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and, filter the measured data obtained by the detector based at least on the determined distribution fitting parameters to thereby obtain noise-filtered measured data.

[0023] Apparatus according to various aspects of the invention may comprise any of the features, combinations of features and / or sub-combinations of features of the methods described herein.

[0024] Obtaining the measured distribution may comprise, for each detection event, obtaining (e.g. measuring) an energy measurement representative of energy deposited by the corresponding particle in the detector.

[0025] Obtaining the measured distribution may comprise, for each detection event: determining a path length associated with a trajectory of the corresponding particle through the detector; and determining the path-length-adjusted energy data for the corresponding particle by normalizing the energy measurement based on thepath length.

[0026] Determining path length associated with a trajectory of the corresponding particle through the detector may comprise determining a trajectory of the corresponding particle through the detector.

[0027] Determining the trajectory of the corresponding particle through the detector may be based on the measured data obtained by the detector.

[0028] Determining the trajectory of the corresponding particle through the detector may comprise determining two three-dimensional locations where the charged particle interacted with the detector.

[0029] Determining the two three-dimensional locations where the charged particle interacted with the detector may be based on the measured data obtained by the detector.

[0030] Obtaining the measured distribution may comprise, for each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

[0031] For each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on the attenuation parameter may comprise scaling (e.g. multiplying) the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

[0032] For each detection event, the attenuation parameter may be based on an expected energy attenuation associated with interaction of the corresponding charged particle with the detector.

[0033] For each detection event, the expected energy attenuation may be based on a location where the corresponding charged particle interacts with the detector.

[0034] For each detection event, determining the location where the corresponding charged particle interacts with the detector may be based on the measured data obtained by the detector.

[0035] For each detection event, the expected energy attenuation may be based on a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

[0036] For each detection event, the expected energy attenuation may be based on a distance between the location where the corresponding charged particle interacts with the detector and the location of the sensor.

[0037] For each detection event, the attenuation parameter may be based on a distance between a location where the corresponding charged particle interacts with the detector and a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

[0038] The first baseline environment may have a high concentration (e.g. flux) of muon particles relative to a concentration (e.g. flux) of beta particles.

[0039] The second baseline environment may have a high concentration (e.g. flux) of beta particles relative to a concentration (e.g. flux) of muon particles.

[0040] The muon detector used to obtain the measured distribution may be of the same type of muon detector used to obtain the first and second baseline distributions.

[0041] Filtering the measured data obtained by the detector may comprise determining a cut-off path-length-adjusted energy value.

[0042] Filtering the measured data obtained by the detector may comprise: keeping, in the noise-filtered measured data, detection events with path-length-adjusted energy values greater than the cut-off path-length-adjusted energy value; and rejecting, from the noise-filtered measured data, detection events with path-length-adjusted energy values less than the cut-off path-length-adjusted energy value.

[0043] Determining the cut-off path-length-adjusted energy value may comprise minimizing a cost function parameterized by the plurality of distribution fitting parameters.

[0044] The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, a portion of the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector.

[0045] The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, a portion of the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

[0046] The cost function may comprise one or more terms that assign cost to rejecting, from the noise filtered measure data, a portion of the plurality of detection events determined, by the fitting of the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interactionof a muon particle with the detector.

[0047] The cost function may comprise one or more terms that assign cost to rejecting, from the noise filtered measure data, a portion of the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

[0048] The plurality of distribution fitting parameters may comprise, for each of the first and second based line distributions, one or more of: a peak location parameter, an amplitude scaling parameter and a variance scaling parameter.

[0049] The method may comprise obtaining timing data associated with the measured data of each detection event and filtering the measured data based on the timing data, wherein the timing data for each detection event comprises information indicative of an estimated transit time of a charged particle through the muon detector.

[0050] Filtering the measured data based on the timing data may comprise, for each detection event, determining an expected time range based at least on a path length of the path of the measured trajectory data and comparing the estimated transit time to the expected time range.

[0051] Comparing the estimated transit time to the expected time range may comprise excluding detection events with transit time outside the expected time range from the noise-filtered measured data and keeping detection events with transit time within the expected time range in the noise-filtered measured data.

[0052] Filtering the measured data based on the timing data may comprise, for each detection event, calculating a particle speed based on the timing data and determining an acceptance range of an expected speed of muons based on the trajectory data and excluding detection events with calculated particle speed outside the acceptance range of the expected speed of muons and keeping detection events with calculated particle speed within the acceptance range of the expected speed of muons.

[0053] The timing data for each detection event may comprise at least a first time component of a first spatiotemporal point corresponding to a point of entry in the detection event and a second time component of a second spatiotemporal point corresponding to a point of exit in the detection event.

[0054] The estimated transit time of the charged particle for a given detection event may be calculated as a difference between the first and second time components of the first and second spatiotemporal points.

[0055] Another aspect of the invention provides a method for filtering noise from measured data obtained by a muon detector, the method comprising: obtaining measured energy data and measured trajectory data for a plurality of detection events, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the measured energy data is representative of energy deposited by the corresponding charged particle in the detector and the measured trajectory data is representative of a path of the corresponding charged particle through the detector; determining, for each detection event, a T-E discriminant value based on the measured energy data and the measured trajectory data corresponding to the de-tection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality of detection events; fitting the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment with a high concentration of muon particles relative to beta particles and the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high con-centration of beta particles relative to muon particles; fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and, filtering the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise-filtered measured data.

[0056] The T-E discriminant value may comprise a scalar value.

[0057] Filtering the measured data obtained by the detector may comprise determining a cut-off T-E discriminant value. Filtering the measured data obtained by the detector may comprise: keeping, in the noise-filtered measured data, detection events with T-E discriminant values that are one of greater than or less than the cutoff T-E discriminant value; and rejecting, from the noise-filtered measured data, detection events with T-E discriminant values that are the other one of greater than or less than the cut-off T-E discriminant value.

[0058] Determining the cut-off T-E discriminant value may comprise minimizing a cost function. The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the firstand second baseline distributions, to be detection events associated with interaction of beta particles with the detector. The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events deter-mined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

[0059] The cost function may comprise one or more terms that assign cost to rejecting, from the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second base-line distributions, to be detection events associated with interaction of a muon particle with the detector. The cost function may comprise one or more terms that assign cost to rejecting, from the noise-filtered measured data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

[0060] Determining, for each detection event, the T-E discriminant value may comprise applying a T-E discriminant determination model to the measured energy data and the measured trajectory data corresponding to the detection event to thereby infer the T-E discriminant value for the detection event.

[0061] The T-E discriminant determination model may comprise a machinelearning model comprising trainable parameters.

[0062] The method may comprise training the machine-learning model. Training the machine-learning model may comprise: initializing values for the trainable parameters; and performing a plurality of training iterations. Each training iteration may comprise: (i) determining, for each detection event in a set of labelled detection event training data, a T-E discriminant value based on current values for the trainable parameters of the T-E discriminant determination model to thereby obtain a corresponding distribution of T-E discriminant values; (ii) determining a T-E discriminant separation parameter for the corresponding distribution of T-E discriminant values, the T-E discriminant separation parameter indicative of which detection events in the corresponding distribution of T-E discriminant values should be retained as being likely muon events and which detection events in the corresponding distribution of T-E discriminant values should be rejected as being unlikely to be muon events; (iii) applying the T-E discriminant separation parameter tothe corresponding distribution of T-E discriminant values to thereby obtain a retained subset of detection events from within the set of labelled detection event data determined by the T-E discriminant determination model as being likely muon events and a rejection subset of detection events from within the set of labelled detection event data determined by the T-E discriminant determination model as being unlikely to be muon events; (iv) determining an evaluation score associated with the current values of the trainable parameters of the T-E discriminant determination model based on labels associated with the set of labelled detection event training data and at least one of: the retained subset of detection events and the rejection subset of detection events; and (v) modifying the values of the trainable parameters of the T-E discriminant determination model.

[0063] For each iteration, the set of labelled detection event training data may comprise: a subset of labelled muon detection training data corresponding to a plurality of detection events associated with a population of muon particles and a subset of labelled beta detection training data corresponding to a plurality of detection events associated with a population of beta particles.

[0064] For each iteration, the set of labelled detection event training data may comprise, for each of a plurality of training detection events: trajectory data, energy data and a label indicating the training detection event to be either a muon event or a beta particle event.

[0065] For each iteration, the set of labelled detection event training data may be different from set of labelled detection event training data used in other iterations.

[0066] For each iteration, the set of labelled detection event training data may be drawn from a larger collection of labelled detection event training data. The larger collection of labelled detection event training data may comprise, for each of a larger plurality of training detection events: trajectory data, energy data and a label indicating the event to be either a muon event or a beta particle event.

[0067] For each iteration the set of labelled detection event training data may be randomly drawn from the larger collection of labelled detection event training data.

[0068] For each iteration, determining the T-E discriminant separation parameter may comprise determining optimizing a cost function to determine an optimal T-E discrimination separation parameter. The cost function may comprise one or more terms attributing cost to at least one of: retaining, in the retained subset, detection events from within the set of labelled detection event data labelled as beta particles orcomprising beta particle labels; and rejecting, in the rejection subset, detection events from within the set of labelled detection event data labelled as muons or comprising muon labels.

[0069] For each iteration, determining the evaluation score may comprise determining an efficiency of separation.

[0070] Determining the efficiency of separation may comprise at least one of: determining a ratio of a number of detection events in the retained subset that are labelled as muons or comprise muon labels to a total number detection events in the set of labelled detection event training data that are labelled as muons or comprise muon labels; and determining a ratio of a number of detection events in the rejection subset that are labelled as beta particles or comprise beta particle labels to a total number detection events in the set of labelled detection evet training data that are labelled as beat particles or comprise beta particle labels.

[0071] For each iteration, determining the evaluation score may comprise determining a purity of separation.

[0072] Determining the purity of separation may comprise at least one of: determining a ratio of a number of detection events in the retained subset that are labelled as muons or comprise muon labels to a total number of detection events in the retained subset; and determining a ratio of a number of detection events in the rejection subset that are labelled as beta particles or comprise beta particle labels to a total number of detection events in the rejection subset.

[0073] For each iteration, modifying the values of the trainable parameters may be based at least in part on the determined evaluation score.

[0074] For each iteration, modifying the values of the trainable parameters may comprise implementing back propagation.

[0075] Each iteration may further comprise evaluating one or more training conclusion conditions and, if the one or more training conclusion conditions are met: ceasing training of the machine-learning model; and determining the machinelearning model with the current values of the trainable parameters to be the T-E discriminant determination model.

[0076] The one or more training conclusion conditions may comprise at least one of: one or more of previously determined evaluation scores exceeding a threshold score; a probability of further improving the evaluation score with further training iterations is below a threshold probability; a change in a number of successiveevaluation scores is below a threshold change; the evaluation score has not improved by more than a threshold amount over a threshold number of training iterations; and a number of training iterations exceeding a threshold number.

[0077] For each detection event, the T-E discriminant value may comprise a path-length-and-attenuation-adjusted (PLAA) energy value.

[0078] For each detection event, the T-E discriminant value may comprise a path-length-adjusted energy data representative of energy deposited by the corresponding per unit path length in the detector.

[0079] Obtaining the measured energy data may comprise, for each detection event, obtaining (e.g. measuring) an energy measurement representative of energy deposited by the corresponding particle in the detector.

[0080] Obtaining the measured energy data may comprise, for each detection event: determining a path length associated with a trajectory of the corresponding particle through the detector; and determining the path-length-adjusted energy data for the corresponding particle by normalizing the energy measurement based on the path length.

[0081] Determining path length associated with a trajectory of the corresponding particle through the detector may comprise determining a trajectory of the corresponding particle through the detector.

[0082] Determining the trajectory of the corresponding particle through the detector may be based on the measured data obtained by the detector.

[0083] Determining the trajectory of the corresponding particle through the detector may comprise determining two three-dimensional locations where the charged particle interacted with the detector. Determining the two three-dimensional locations where the charged particle interacted with the detector may be based on the measured data obtained by the detector.

[0084] Obtaining the measured energy data may comprise, for each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

[0085] For each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on the attenuation parameter may comprise scaling (e.g. multiplying) the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

[0086] For each detection event, the attenuation parameter may be based on an expected energy attenuation associated with interaction of the corresponding charged particle with the detector.

[0087] For each detection event, the expected energy attenuation may be based on a location where the corresponding charged particle interacts with the detector.

[0088] For each detection event, determining the location where the corresponding charged particle interacts with the detector may be based on the measured data obtained by the detector.

[0089] For each detection event, the expected energy attenuation may be based on a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

[0090] For each detection event, the expected energy attenuation may be based on a distance between the location where the corresponding charged particle interacts with the detector and the location of the sensor.

[0091] For each detection event, the attenuation parameter may be based on a distance between a location where the corresponding charged particle interacts with the detector and a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

[0092] The first baseline environment may have a high concentration (e.g. flux) of muon particles relative to a concentration (e.g. flux) of beta particles.

[0093] The second baseline environment may have a high concentration (e.g. flux) of beta particles relative to a concentration (e.g. flux) of muon particles.

[0094] The mu-on detector used to obtain the measured distribution may be of the same type of muon detector used to obtain the first and second baseline distributions.

[0095] Filtering the measured data obtained by the detector may comprise determining a cut-off path-length-adjusted energy value.

[0096] Filtering the measured data obtained by the detector may comprise: keeping, in the noise-filtered measured data, detection events with path-length-adjusted energy values greater than the cut-off path-length-adjusted energy value; and rejecting, from the noise-filtered measured data, detection events with path-length-adjusted energy values less than the cut-off path-length-adjusted energy value.

[0097] Determining the cut-off path-length-adjusted energy value may compriseminimizing a cost function parameterized by the plurality of distribution fitting parameters.

[0098] The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector. The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

[0099] The cost function may comprise one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the fitting of the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of a muon particle with the detector. The cost function may comprise one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

[0100] The plurality of distribution fitting parameters may comprise, for each of the first and second based line distributions, one or more of: a peak location parameter, an amplitude scaling parameter and a variance scaling parameter.

[0101] The method may comprise obtaining timing data associated with the measured data of each detection event. Determining the T-E discriminant value for each detection event may be based on measured energy data, the measured trajectory data and the measured timing data corresponding to the detection event to thereby infer the T-E discriminant value for the detection event.

[0102] For each detection event, the measured timing data may comprise information that allows the determination of an estimated transit time of the charged particle through the muon detector.

[0103] The method may comprise obtaining timing data associated with the measured data of each detection event and filtering the measured data based on the timing data. The timing data for each detection event comprises information indicativeof an estimated transit time of a charged particle through the muon detector.

[0104] Filtering the measured data based on the timing data may comprise, for each detection event, determining an expected time range based at least on the path length of the detection event and comparing the estimated transit time to the expected time range.

[0105] Comparing the estimated transit time to the expected time range may comprise excluding detection events with transit time outside the expected time range from the noise-filtered measured data and keeping detection events with transit time within the expected time range in the noise-filtered measured data.

[0106] Filtering the measured data based on the timing data may comprise, for each detection event, calculating a particle speed based on the timing data and determining an acceptance range of an expected speed of muons based on the trajectory data and excluding detection events with calculated particle speed outside the acceptance range of the expected speed of muons and keeping detection events with calculated particle speed within the acceptance range of the expected speed of muons.

[0107] The timing data for each detection event may comprise at least a first time component of a first spatiotemporal point corresponding to a point of entry in the detection event and a second time component of a second spatiotemporal point corresponding to a point of exit in the detection event.

[0108] The estimated transit time of the charged particle for a given detection event may be calculated as a difference between the first and second time components of the first and second spatiotemporal points.

[0109] Another aspect of the invention provides an apparatus for filtering measured data obtained by a muon detector where the measured data comprises a plurality of detection events, each detection event associated with interaction of a corresponding charged particle with the muon detector. The apparatus comprises: an energy sensing system for determining, for each detection event, a measured energy deposited by the corresponding particle in the muon detector; a processor connected to the energy sensing system to receive, for each detection event, the measured energy. The processor is configured to: determine, for each detection event, a measured trajectory representative of a path of the corresponding particle through the muon detector; determine, for each detection event, a T-E discriminant value based on the measured energy data and the measured trajectory data corresponding to thedetection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality of detection events; fit the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment with a high concentration of muon particles relative to beta particles and the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high concentration of beta particles relative to muon particles and fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and, filter the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise-filtered measured data.

[0110] Apparatus according to various aspects of the invention may comprise any of the features, combinations of features and / or sub-combinations of features of the methods described herein.

[0111] Another aspect of the invention provides a method for filtering noise from measured data obtained by a muon detector. The method comprises: obtaining measured energy data and measured trajectory data for a plurality of detection events, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the measured energy data is representative of energy deposited by the corresponding charged particle in the detector and the measured trajectory data is representative of a path of the corresponding charged particle through the detector; providing the measured energy data and the measured trajectory data as in-puts into a machine learning algorithm, wherein the machine learning algorithm is trained to assign, as an output, a probability value to each detection event based on the corresponding measured energy data and measured trajectory data of the detection event, wherein the probability value reflects the probability of the corresponding detection event being a muon detection event; and, filtering or weighting the measured data obtained by the detector based at least on the probability values associated with the plurality of detection events to thereby obtain noise-filtered measured data.

[0112] Apparatus according to various aspects of the invention may comprise any of the features, combinations of features and / or sub-combinations of features of the methods described herein.

[0113] Another aspect of the invention provides a method for filtering noise from measured data obtained by a muon detector. The method comprises obtaining measured energy data, measured trajectory data and measured timing data for a plurality of detection events, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the measured energy data is representative of energy deposited by the corresponding charged particle in the detector, the measured trajectory data is representative of a path of the corresponding charged particle through the detector, and the measured timing data is indicative of an estimated transit time of the charged particle through the detector; determining, for each detection event, a T-E discriminant value based on the measured energy data, the measured trajectory data and the measured timing data corresponding to the detection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality of detection events; fitting the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein: the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and, filtering the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise-filtered measured data.

[0114] For each detection event, an expected time rage may be determined based at least in part on a path length of the path of the measured trajectory data and the expected time range may be incorporated into the T-E discriminant value.

[0115] Filtering the measured data obtained by the detector may comprise determining a cut-off T-E discriminant value.

[0116] Filtering the measured data obtained by the detector may comprise: keeping, in the noise-filtered measured data, detection events with T-E discriminant values that are one of greater than or less than the cut-off T-E discriminant value; and rejecting, from the noise-filtered measured data, detection events with T-E discriminant values that are the other one of greater than or less than the cut-off T-Ediscriminant value.

[0117] Determining the cut-off T-E discriminant value may comprise minimizing a cost function.

[0118] The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector.

[0119] The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

[0120] The cost function may comprise one or more terms that assign cost to rejecting, from the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of a muon particle with the detector.

[0121] The cost function may comprise one or more terms that assign cost to rejecting, from the noise-filtered measured data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

[0122] Determining, for each detection event, the T-E discriminant value may comprise applying a T-E discriminant determination model to the measured energy data, the measured trajectory data and the measured timing data corresponding to the detection event to thereby infer the T-E discriminant value for the detection event.

[0123] The T-E discriminant determination model may comprise a machinelearning model comprising trainable parameters.

[0124] The method may comprise training the machine-learning model. Training the machine-learning model may comprise: initializing values for the trainable parameters; and performing a plurality of training iterations, each training iteration comprising: (i) determining, for each detection event in a set of labelled detection event training data, a T-E discriminant value based on current values for the trainable parameters of the T-E discriminant determination model to thereby obtain acorresponding distribution of T-E discriminant values; (ii) determining a T-E discriminant separation parameter for the corresponding distribution of T-E discriminant values, the T-E discriminant separation parameter indicative of which detection events in the corresponding distribution of T-E discriminant values should be retained as being likely muon events and which detection events in the corresponding distribution of T-E discriminant values should be rejected as being unlikely to be muon events; (iii) applying the T-E discriminant separation parameter to the corresponding distribution of T-E discriminant values to thereby obtain a retained subset of detection events from within the set of labelled detection event data determined by the T-E discriminant determination model as being likely muon events and a rejection subset of detection events from within the set of labelled detection event data determined by the T-E discriminant determination model as being unlikely to be muon events; (iv) determining an evaluation score associated with the current values of the trainable parameters of the T-E discriminant determination model based on labels associated with the set of labelled detection event training data and at least one of: the retained subset of detection events and the rejection subset of detection events; and (v) modifying the values of the trainable parameters of the T-E discriminant determination model.

[0125] For each iteration, the set of labelled detection event training data may comprise: a subset of labelled muon detection training data corresponding to a plurality of detection events associated with a population of muon particles and a subset of labelled beta detection training data corresponding to a plurality of detection events associated with a population of beta particles.

[0126] For each iteration, the set of labelled detection event training data may comprise, for each of a plurality of training detection events: trajectory data, energy data, timing data and a label indicating the training detection event to be either a muon event or a beta particle event.

[0127] For each iteration, the set of labelled detection event training data may be different from set of labelled detection event training data used in other iterations.

[0128] For each iteration, the set of labelled detection event training data may be drawn from a larger collection of labelled detection event training data, wherein the larger collection of labelled detection event training data comprises, for each of a larger plurality of training detection events: trajectory data, energy data, timing data and a label indicating the event to be either a muon event or a beta particle event.

[0129] For each iteration the set of labelled detection event training data may be randomly drawn from the larger collection of labelled detection event training data.

[0130] For each iteration, determining the T-E discriminant separation parameter may comprise determining optimizing a cost function to determine an optimal T-E discrimination separation parameter.

[0131] The cost function may comprise one or more terms attributing cost to at least one of: retaining, in the retained subset, detection events from within the set of labelled detection event data labelled as beta particles or comprising beta particle labels; and rejecting, in the rejection subset, detection events from within the set of labelled detection event data labelled as muons or comprising muon labels.

[0132] For each iteration, determining the evaluation score may comprise determining an efficiency of separation.

[0133] Determining the efficiency of separation may comprise at least one of: determining a ratio of a number of detection events in the retained subset that are labelled as muons or comprise muon labels to a total number detection events in the set of labelled detection evet training data that are labelled as muons or comprise muon labels; and, determining a ratio of a number of detection events in the rejection subset that are labelled as beta particles or comprise beta particle labels to a total number detection events in the set of labelled detection evet training data that are labelled as beat particles or comprise beta particle labels.

[0134] For each iteration, determining the evaluation score may comprise determining a purity of separation.

[0135] Determining the purity of separation may comprise at least one of: determining a ratio of a number of detection events in the retained subset that are labelled as muons or comprise muon labels to a total number of detection events in the retained subset; and, determining a ratio of a number of detection events in the rejection subset that are labelled as beta particles or comprise beta particle labels to a total number of detection events in the rejection subset.

[0136] For each iteration, modifying the values of the trainable parameters may be based at least in part on the determined evaluation score.

[0137] For each iteration, modifying the values of the trainable parameters may comprise implementing back propagation.

[0138] Each iteration may further comprise evaluating one or more training conclusion conditions and, if the one or more training conclusion conditions are met:ceasing training of the machine-learning model; and determining the machinelearning model with the current values of the trainable parameters to be the T-E discriminant determination model.

[0139] The one or more training conclusion conditions may comprise at least one of: one or more of previously determined evaluation scores exceeding a threshold score; a probability of further improving the evaluation score with further training iterations is below a threshold probability; a change in a number of successive evaluation scores is below a threshold change; the evaluation score has not improved by more than a threshold amount over a threshold number of training iterations; and a number of training iterations exceeding a threshold number.

[0140] For each detection event, the T-E discriminant value may comprise a path-length-and-attenuation-adjusted (PLAA) energy value.

[0141] For each detection event, the T-E discriminant value may comprise a path-length-adjusted energy data representative of energy deposited by the corresponding per unit path length in the detector.

[0142] Obtaining the measured energy data may comprise, for each detection event, obtaining (e.g. measuring) an energy measurement representative of energy deposited by the corresponding particle in the detector.

[0143] Obtaining the measured energy data may comprise, for each detection event: determining a path length associated with a trajectory of the corresponding particle through the detector; and determining the path-length-adjusted energy data for the corresponding particle by normalizing the energy measurement based on the path length.

[0144] Determining path length associated with a trajectory of the corresponding particle through the detector may comprise determining a trajectory of the corresponding particle through the detector.

[0145] Determining the trajectory of the corresponding particle through the detector may be based on the measured data obtained by the detector.

[0146] Determining the trajectory of the corresponding particle through the detector may comprise determining two three-dimensional locations where the charged particle interacted with the detector.

[0147] Determining the two three-dimensional locations where the charged particle interacted with the detector may be based on the measured data obtained by the detector.

[0148] Obtaining the measured energy data may comprise, for each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

[0149] For each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on the attenuation parameter may comprise scaling (e.g. multiplying) the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

[0150] For each detection event, the attenuation parameter may be based on an expected energy attenuation associated with interaction of the corresponding charged particle with the detector.

[0151] For each detection event, the expected energy attenuation may be based on a location where the corresponding charged particle interacts with the detector.

[0152] For each detection event, determining the location where the corresponding charged particle interacts with the detector may be based on the measured data obtained by the detector.

[0153] For each detection event, the expected energy attenuation may be based on a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

[0154] For each detection event, the expected energy attenuation may be based on a distance between the location where the corresponding charged particle interacts with the detector and the location of the sensor.

[0155] For each detection event, the attenuation parameter may be based on a distance between a location where the corresponding charged particle interacts with the detector and a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

[0156] The first baseline environment may have a high concentration (e.g. flux) of muon particles relative to a concentration (e.g. flux) of beta particles.

[0157] The second baseline environment may have a high concentration (e.g. flux) of beta particles relative to a concentration (e.g. flux) of muon particles.

[0158] The muon detector used to obtain the measured distribution may be of the same type of muon detector used to obtain the first and second baseline distributions.

[0159] Filtering the measured data obtained by the detector may comprise determining a cut-off path-length-adjusted energy value.

[0160] Filtering the measured data obtained by the detector may comprise: keeping, in the noise-filtered measured data, detection events with path-length-adjusted energy values greater than the cut-off path-length-adjusted energy value; and rejecting, from the noise-filtered measured data, detection events with path-length-adjusted energy values less than the cut-off path-length-adjusted energy value.

[0161] Determining the cut-off path-length-adjusted energy value may comprise minimizing a cost function parameterized by the plurality of distribution fitting parameters.

[0162] The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector.

[0163] The cost function may comprise one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

[0164] The cost function may comprise one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the fitting of the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of a muon particle with the detector.

[0165] The cost function may comprise one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

[0166] The plurality of distribution fitting parameters may comprise, for each of the first and second based line distributions, one or more of: a peak location parameter, an amplitude scaling parameter and a variance scaling parameter.

[0167] The measured data may comprise a plurality of detection events, each detection event associated with interaction of a corresponding charged particle with the muon detector. The apparatus comprises: an energy sensing system fordetermining, for each detection event, a measured energy deposited by the corresponding particle in the muon detector; a timing system for determining, for each detection event, timing data indicative of an estimated transit time of the charged particle through the muon detector; a processor connected to the energy sensing system and the timing system to receive, for each detection event, the measured energy and the measured timing data, the processor configured to: determine, for each detection event, a measured trajectory representative of a path of the corresponding particle through the muon detector; determine, for each detection event, a T-E discriminant value based on the measured energy data, the measured trajectory data and the measured timing data corresponding to the detection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality of detection events; fit the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein: the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and, filter the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise-filtered measured data.

[0168] Apparatus according to various aspects of the invention may comprise any of the features, combinations of features and / or sub-combinations of features of the methods described herein.

[0169] Aspects of the invention provide apparatus having any new and inventive feature, combination of features, or sub-combination of features as described herein.

[0170] Aspects of the invention provide methods having any new and inventive steps, acts, combination of steps and / or acts or sub-combination of steps and / or acts as described herein.

[0171] It is emphasized that the invention relates to all combinations of the above features, even if these are recited in different claims.

[0172] Further aspects and example embodiments are illustrated in the accompanying drawings and / or described in the following description.Brief Description of the Drawings

[0173] The accompanying drawings illustrate non-limiting example embodiments of the invention.

[0174] FIG. 1 A is a schematic partial perspective view of a cross-section of a prior art borehole muon detector.

[0175] FIG. 1 B is a schematic partial perspective view of a cross-section of another prior art borehole muon detector.

[0176] FIG. 2A is a histogram chart showing the count of detection events corresponding to a range of zenith angle values (0) generated by a muon detector in a controlled laboratory environment.

[0177] FIG. 2B is another histogram chart showing the count of detection events corresponding to a range of zenith angle values (0) generated by the same muon detector when deployed on-site in a borehole.

[0178] FIG. 3 is a schematic flowchart of a method for filtering noise in trajectory data obtained by muon detectors according to an example embodiment.

[0179] FIGs. 4A, 4B, 4G and 4D (collectively, FIG. 4) are exemplary plots of path length and attenuation-adjusted (PLAA) energy data distributions exhibiting characteristics measured by a muon detector. FIG. 4A is an exemplary distribution taken from a muon detector deployed underground in a borehole. FIG. 4B is an exemplary distribution in a controlled environment dominated by beta particles. FIG.4C is an exemplary distribution in a controlled environment dominated by muon particles. FIG. 4D shows how the distribution of FIG. 4A may be fit to the distributions of FIGs. 4B and 4C.

[0180] FIG. 5 is a schematic flowchart of a method for filtering noise in trajectory data obtained by muon detectors according to another example embodiment.

[0181] FIG. 6 is a schematic flowchart of a method of iterative training of a machine learning algorithm to optimize a T-E discriminant determination model according to an example embodiment.

[0182] FIG. 7 is a schematic flowchart of a method for filtering noise in trajectory data obtained by muon detectors according to another example embodiment.Detailed Description

[0183] Throughout the following description, specific details are set forth in order to provide a more thorough understanding of the invention. However, the invention may be practiced without these particulars. In other instances, well known elementshave not been shown or described in detail to avoid unnecessarily obscuring the invention. Accordingly, the specification and drawings are to be regarded in an illustrative, rather than a restrictive sense.

[0184] Methods and apparatus are provided for filtering noise from measured data obtained by a muon detector.

[0185] The methods and apparatus according to some aspects of the invention comprise: obtaining a measured distribution of path-length-adjusted energy data for a plurality of detection events associated with the measured data, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the path-length-adjusted energy data is representative of energy deposited by the corresponding particle per unit path length in the detector; fitting (e.g. by a processor) the measured distribution to first and second baseline distributions of deposition energy per unit path length wherein: the first baseline distribution of deposition energy per unit path length is obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; the second baseline distribution of deposition energy per path length is obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributions comprises determining (e.g. by the processor) a plurality of distribution fitting parameters; and, filtering (e.g. by the processor) the measured data obtained by the detector based at least on the determined distribution fitting parameters to thereby obtain noise-filtered measured data.

[0186] The methods and apparatus according to some aspects of the invention comprise: obtaining measured energy data, measured trajectory data and optionally timing data for a plurality of detection events, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the measured energy data is representative of energy deposited by the corresponding charged particle in the detector, the measured trajectory data is representative of a path of the corresponding charged particle through the detector, and the timing data is indicative of an estimated transit time of the charged particle through the detector; determining, for each detection event, a T-E discriminant value based on the measured energy data, the measured trajectory data and optionally timing data corresponding to the detection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality ofdetection events; fitting the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment with a high concentration of muon particles relative to beta particles and the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and, filtering the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise-filtered measured data.

[0187] FIG. 3 is a schematic flowchart of a method 100 for filtering noise in trajectory data obtained by muon detectors according to an example embodiment. Method 100 can be applied to filter noise in any suitable muon detectors, including, but not limited to, muon detectors comprising sub-detector elements sensitive to charged particles (e.g. scintillator elements). While the methods and systems described herein are particularly suitable for borehole muon detectors deployed underground (e.g. the borehole muon detectors of FIGs. 1A, 1 B), unless expressly indicated, the methods and systems described herein are not limited to any particular type of muon detector or to any particular application of a muon detector.

[0188] Method 100 may be performed by one or more suitably configured processor(s) 101. Processor(s) 101 may be embedded in a muon detector (e.g. one of muon detectors 10A, 10B described above, although that is not necessary) or operatively coupled to, e.g. in data communication with, one or more muon detectors to receive data therefrom. Method 100 may begin with a sub-routine 110. In some embodiments, sub-routine 110 is performed for each detection event. As used herein, a detection event corresponds to a determination, by a muon detector (including any suitably connected and configured processor(s)), that a charged particle has interacted with the muon detector and, typically, a determination of a corresponding trajectory of the charged particle as it traverses the muon detector. For some particular muon detectors (such as, for example, the detectors of FIGs. 1 A and 1 B), a detection event may comprise a scenario where at least two discrete spatiotemporal points (x,y,z,t) can be identified within a maximum given time window defined to fully capture signals that might arise from the passage of a muon, to allow a trajectory (3Dline) to be estimated from the spatial coordinates (x,y,z) of the two spatiotemporal points. In some cases, each of the two spatiotemporal points may be detected by a distinct sub-detector element. During deployment, a muon detector may identify a plurality of detection events each associated with corresponding trajectory data and optionally timing data.

[0189] For a given detection event, sub-routine 110 begins with block 114 which involves obtaining trajectory data 112 and optionally timing data 113 for the corresponding detection event. Trajectory data 112 and optional timing data 113 may be generated by the muon detector (including any suitably connected and configured processor(s) 101) and comprise information obtained by the muon detector that allows a trajectory of a charged particle to be estimated. Timing data 113 may be obtained by any suitable timing system. Timing data 113 comprise information that allows, for the corresponding detection event, an estimated transit time of a charged particle through the muon detector to be determined. “Transit time” of a charged particle through the muon detector, as used herein, is the elapsed time for a charged particle to traverse the muon detector from a point of entry to a point of exit. In some embodiments, timing data 113 comprise information that allows the time component t of each of the spatiotemporal points (x,y,z,t) associated with the exit and entry points in a detection event to be determined. In some embodiments, timing data 113 comprise time stamps associated with photodetectors measuring scintillation light from scintillator elements. In some embodiments, trajectory data 112 comprises information that allows one or more of the following parameters to be determined:• entry point of the particle into the detector (or any other suitable first point of interaction between the particle and the detector);• exit point of the particle out of the detector (or any other suitable second point of interaction between the particle and the detector);• an azimuthal angle of the trajectory relative to a longitudinal axis (or any other suitable geometrical or orientation axis) of the muon detector;• a zenith angle of the trajectory relative to the longitudinal axis (or any other suitable geometrical or orientation axis) of the muon detector;• etc.

[0190] Trajectory data 112 may be generated by any suitable muon detectors by any suitable means. In a non-limiting example embodiment, trajectory data 112 are generated by muon detectors comprising sub-detector elements sensitive to chargedparticles (e.g. scintillator fibers and / or scintillator bars). For simplicity, the term “trajectory data 112” is used herein to refer to both trajectory data 112 associated with a single detection event as well as aggregate trajectory data 112 corresponding to a plurality of detection events.

[0191] Sub-routine 110 then proceeds to block 118 which comprises obtaining deposited energy data 116 (energy data 116, for brevity) from the muon detector for the corresponding detection event. Energy data 116 may be generated by the muon detector (including any suitably connected and configured processor(s) 101). Energy data 116 of a detection event is associated with trajectory data 112 of the same detection event - that is, each detection event may have an associated trajectory 112 and associated energy data 116. In some embodiments, energy data 116 comprises a measurement correlated with energy deposited by a particle as it interacts with the muon detector. For example, where the sub-detector elements of a muon detector comprise scintillator elements, energy data 116 may comprise the output of photodetectors, electrical current sensors and / or the like connected to measure scintillation light in the scintillator elements which is correlated with the energy deposited in the scintillator elements. In some embodiments, energy data 116 comprise information about the amount of energy (e.g. light energy) detected at photodetectors of a muon detector for a given detection event. For simplicity, the term “energy data 116” is used herein to refer to both energy data 116 associated with a single corresponding detection event as well as the aggregate energy data 116 corresponding to a plurality of detection events.

[0192] Sub-routine 110 then proceeds to block 124 which comprises adjusting (e.g. normalizing) energy data 116 for a particular detection event based on a path length of the estimated trajectory provided by trajectory data 112 to generate path-length-adjusted energy data 122. As discussed above, a charged particle that traverses the muon detector on a trajectory with a relatively long path length through the detector can deposit more energy into the detector compared to a particle that traverses the muon detector on a trajectory with a relatively short path length through the detector. However, because the total kinetic energy of beta particles is fundamentally constrained by the energy conservation endpoint (typically up to a few MeV) of the radioactive decay from which the beta particle originates, beta particles that penetrate the detector to create an apparent muon track may preferentially deposit their energy at a lower rate per unit path length through the detectorcompared to muon particles. Therefore, block 124 may be performed to normalize energy data 116 with respect to path length to thereby make path-length-adjusted energy data 122 relatively more comparable as between detection events.

[0193] In some embodiments, the block 124 adjustment (normalization) comprises: determining (based on trajectory data 112) a path-length parameter correlated with the path length through a muon detector of a particular trajectory 112 of a particular detection event; and dividing energy data 116 of the particular detection event by the path length parameter. It will be appreciated that determining the path length parameter based on the trajectory data 112 will depend on the geometry of a particular muon detector and possibly on the geometries of the subdetector elements of the muon detector.

[0194] Sub-routine 110 then proceeds to optional block 128 which involves further adjusting path-length-adjusted energy data 122 based on an optional attenuation parameter correlated with energy attenuation in the muon detector to obtain path length and attenuation-adjusted (PLAA) energy data 126. As described elsewhere herein, PLAA energy data 126 is an example of a T-E discriminant value. As alluded to above, attenuation of detected energy associated with a detection event in a muon detector may depend on a location that a particle impinges on the muon detector or the scintillator element (referred to herein as the “interaction location”). In the case of the above discussed muon detectors 10A, 10B, for example, the distance between a charged particle interaction with a scintillator element and the sensor used to measure the scintillation associated with this interaction can influence the amount of detected energy because of attenuation of the scintillation light energy between the interaction location and the sensor. In particular embodiments, which use photodetectors to measure the energy associated with scintillation in scintillator subdetector elements, detected light energy at the photodetector depends on the interaction location and more specifically on the distance (and the corresponding amount of attenuation) between the interaction location where the particle intersects the sub-detector element and the closest photodetector (also referred to as “detection distance” herein).

[0195] In some embodiments, for each detection event, the block 128 adjustment involves scaling (e.g. multiplying) the corresponding path-length adjusted energy data 122 by an attenuation parameter that is correlated with (e.g. proportional to) expected energy attenuation in the muon detector to obtain path length and attenuation-adjusted energy data 126. In some embodiments, this attenuation parameter is correlated with (e.g. proportional to) an expected amount of attenuation between the interaction event and a corresponding sensor. In some embodiments, this attenuation parameter is correlated with (e.g. proportional to) a distance between the interaction location and the sensor.

[0196] Path length and attenuation-adjusted energy data 126 may be referred to as PLAA energy data 126 herein. PLAA energy data 126 may be understood as the specific energy loss of the corresponding particle per path length that is further scaled by the attenuation parameter to account for energy attenuation. As discussed in the above example, the longer the detection distance, the more energy may be lost before reaching the photodetectors. Therefore, block 128 may be performed to normalize path-length-adjusted energy data 122 with respect to the detection distance to thereby generate PLAA energy data 126, which is comparable as between detection events regardless of path length of the trajectory and detection distance.

[0197] It should be understood that block 124 and block 128 may be performed in any suitable order to generate PLAA energy data 126. Specifically, it is not necessary to perform block 124 prior to block 128 as shown in FIG. 3. In some embodiments, block 128 is performed prior to block 124. Furthermore, it should be understood that one or more steps of sub-routine 110 corresponding to blocks 114, 118, 124 and 128 may be optional in sub-routine 110. For example, in some embodiments, trajectory data 112 and / or energy data 116 are already collected and available for processing and sub-routine 110 may simply perform blocks 124 and 128 for each detection event.

[0198] Sub-routine 110 may be performed for each detection event in a collection of a plurality of detection events. PLAA energy data 126 of charged particles exhibits statistical fluctuations due to the stochastic nature of energy loss mechanisms.Therefore, given a plurality of detection events and a plurality of associated PLAA energy data 126 values, a measured distribution 130 of PLAA energy data 126 may be obtained.

[0199] FIG. 4A is a plot 200A of an example measured distribution 130 of PLAA energy data 126. As can be seen from FIG. 4A, measured distribution 130 exhibits two notable peaks 201 and 203. Peak 201 occurs at a PLAA energy value that is relatively small compared to peak 203, suggesting the presence of trajectory data that has been measured due to beta particles.

[0200] Returning to FIG. 3, after completing sub-routine 110 for each detection event in a plurality of detection events, method 100 proceeds to block 134 which comprises obtaining baseline distributions 132 and measured distribution 130. As discussed above, measured distribution 130 may be generated from sub-routine 110 of method 100.

[0201] Baseline distributions 132 (as used herein) refer to distributions of PLAA energy values obtained for specific charged particles (e.g. muon particles, beta particles, etc.) in a controlled environment or within a defined sub-sample of the PLAA data such that each baseline distribution 132 of PLAA energy values is primarily the result of a specific desired charged particle. FIG. 4B is a plot 200B of an example baseline distribution 132B of PLAA energy values obtained for beta particles in a controlled environment for beta particles. FIG. 4G is a plot 200C of an example baseline distribution 132M of PLAA energy values obtained for muon particles in a controlled environment for muon particles. As can be seen from FIG. 4B and FIG. 4C, beta particles and muon particles have distinct baseline distributions 132 of PLAA energy values due to the inherent difference in their energy deposition profiles.

[0202] After obtaining baseline distributions 132 (e.g. baseline beta particle distribution 132B and baseline muon particle distribution 132M) and measured distribution 130, method 100 proceeds to block 136 which comprises fitting measured distribution 130 to baseline distributions 132 by any suitable fitting methodology. Block 136 is based on the assumption that measured distribution 130 is a result of contribution from both baseline beta particle distribution 132B and baseline muon particle distribution 132M and, that, consequently, measured distribution 130 can be estimated as a combination of baseline beta particle distribution 132B and baseline muon particle distribution 132M. For example, as shown in plot 200D of FIG. 4D, measured distribution 130 can be fitted as a combination of curve-fitted baseline beta particle distribution 132B* and baseline muon particle distribution 132M* (shown in dashed lines in FIG. 4D) respectively scaled by corresponding curve-fitting parameters.

[0203] Block 136 may comprise any suitable curve fitting technique comprising any suitable set of curve-fitting parameters. The output of the block 136 curve-fitting process may be a set of curve-fitting parameter values140. In a non-limiting example embodiment, curve-fitting parameters 140 comprise a first constant multiplier for baseline beta particle distribution 132B and a second constant multiplier for baselinemuon particle distribution 132M.

[0204] Method 100 then proceeds to a sub-routine 150 for filtering noise from data 112 obtained by the muon detector to generate noise-filtered trajectory data 170. In the particular case of the illustrated embodiment, sub-routine 150 comprises: determining a particular PLAA value 164 (referred to herein as the “cut-off PLAA energy value” 164 - see FIG. 4D); and filtering measured PLAA distribution 130 by removing, from consideration, detection events associated with PLAA energy values below cut-off PLAA value 164 to arrive at noise-filtered trajectory data 170. As discussed below, as compared to the measured data prior to filtering (e.g. measured PLAA distribution 130), noise-filtered trajectory data 170 will have a relatively high fraction of detection events corresponding to muons and a relatively low fraction of detection events corresponding to beta particles.

[0205] Sub-routine 150 of the illustrated embodiment begins with block 152 which involves generating a cost function which may be used for determining an optimal cutoff PLAA energy value 164. The block 152 cost function may comprise a function of PLAA energy value (as the variable) and may be parameterized at least by curvefitting parameter values 140. The block 152 cost function may have terms that assign cost to: undesirably keeping detection events that may be results of beta energy deposition; and, undesirably filtering (i.e. removing) detection events that may be results of muon energy deposition.

[0206] Sub-routine 150 then proceeds to block 154, which involves determining an optimal cut-off PLAA energy value 164. Block 154 may comprise selecting a cutoff PLAA energy value 164 that minimizes the block 152 cost function. Block 166 comprises using the block 154 cut-off PLAA energy value 164 and optionally timing data 113 to filter the measured trajectory data 112 (e.g. detection events) to thereby obtain noise-filtered trajectory data 170.

[0207] Referring again to FIG. 4D, cut-off PLAA energy value 164 is indicated by a dotted-and-dashed line in diagram 200D and the direction of the arrow of the dotted-and-dashed line indicates the portion of measured PLAA energy distribution 130 that is kept by the block 166 filtering process - i.e. detection events corresponding to PLAA values greater than cut-off PLAA energy value 164 are maintained in noise-filtered trajectory data 170. Detection events belonging to the portion of measured PLAA energy distribution 130 less than cut-off PLAA energy value 164 (which may be referred to as “detection noise” herein) are filtered out ofnoise-filtered trajectory data 170. Because energy data 116, and consequently the PLAA energy value 126 of each detection event, is associated with the corresponding trajectory data 112, after block 154 of determining cut-off PLAA value 164, method 100 performs block 166 to filter (i.e. remove) detection noise from trajectory data 112 to thereby generate noise-filtered trajectory data 170.

[0208] In some embodiments, the steps in sub-routine 150 (e.g. determining a particular cut-off PLAA energy value 164; and filtering measured PLAA distribution 130 by removing, from consideration, detection events associated with PLAA energy values below cut-off PLAA value 164 to arrive at noise-filtered trajectory data 170. may be performed using other techniques. For example, in some embodiments, detection events in measured PLAA distribution 130 that are at least n standard deviations away from the mean of fitted baseline muon particle distribution 132M* and / or also within m standard deviations of fitted baseline beta particle distribution 132B* may be identified as beta particle deposition and subsequently removed from trajectory data 112, where n, m can be any number greater than zero.

[0209] In some embodiments, trajectory data 112 is additionally filtered on the basis of timing data 113 at block 166. As discussed above, in some scenarios, multiple beta particles may enter the muon detector at different positions within a time window such that their collective interactions mimic the energy deposition signature (sometimes including path-length-adjusted energy deposition signature and / or PLAA signature) of a muon particle traversing the detector. However, because muon particles travel at expected muon speeds near the speed of light, the time difference between an entry interaction and an exit interaction of any muon particle traversing the detector is constrained to an expected time range. The expected time range is based at least on the path length of the particle through the detector, and optionally on the measurement uncertainty of the timing system used to obtain timing data 113 (e.g. a few hundred picoseconds). The expected time range is configurable for each detection event given the variable path length of the particle from detection event to detection event. In some embodiments, trajectory data 112 is additionally filtered by excluding detection events with transit time outside the expected time range of the corresponding detection event and keeping detection events with transit time consistent with the expected time range of the corresponding detection event. In some embodiments, for each detection event, a particle speed is calculated based on trajectory data 112 and timing data 113. In some embodiments, comparing theexpected speed of muons to the calculated particle speed for each detection event comprises defining an acceptance range for the expected speed of muons. In some embodiments, the acceptance range for the detection event is based at least in part on the measurement uncertainty in the timing system used to obtain timing data 113. In some embodiments, trajectory data 112 is additionally filtered by excluding detection events with calculated particle speed outside the acceptance range of the expected speed of muons from the noise-filtered measured data and keeping detection events with calculated particle speed within the acceptance range of the expected speed of muon particles in the noise-filtered trajectory data. Thus, trajectory data 112 can be additionally filtered to eliminate such “multi-beta” false-positive tracks based on timing data 113.

[0210] Other additional or alternative filtering technique(s) may also be applied at block 166. For example, for muon detectors deployed underground, most muons are expected to arrive at the muon detectors from a side of the muon detector closer to the surface of the earth, whereas particles arriving at the muon detectors from below the detector (i.e. a side of the detector further from the surface of the earth) are somewhat more likely to be beta particles due to the presence of beta particle sources in earth. Consequently, in regions of the measured PLAA distribution 130 where fitted baseline muon particle distribution 132M* and fitted baseline beta particle distribution 132B* overlap, trajectory data 112 may be additionally or alternatively filtered on the basis of the orientation of the trajectory (i.e. the location of the entry and exit points of the given trajectory through the muon detector).

[0211] FIG. 5 is a schematic flowchart of a method 300 for filtering noise in trajectory data obtained by muon detectors according to another example embodiment. Method 300 can be applied to filter noise in any suitable muon detectors, including, but not limited to, muon detectors comprising sub-detector elements sensitive to charged particles (e.g. scintillator elements). While the methods and systems described herein are particularly suitable for borehole muon detectors deployed underground (e.g. the borehole muon detectors of FIGs. 1A, 1 B), unless expressly indicated, the methods and systems described herein are not limited to any particular type of muon detector or to any particular application of a muon detector.

[0212] Method 300 may be performed by one or more suitably configured processor(s) 301. Processor(s) 301 may be embedded in a muon detector (e.g. one of muon detectors 10A, 10B described above, although that is not necessary) oroperatively coupled to, e.g. in data communication with, one or more muon detectors to receive data therefrom. Method 300 may begin with a sub-routine 310. In some embodiments, sub-routine 310 is performed for each detection event.

[0213] For a given detection event, sub-routine 310 begins with block 314 which involves obtaining trajectory data 312 and optionally timing data 313 for the corresponding detection event. Trajectory data 312 and timing data 313 may be generated by the muon detector (including any suitably connected and configured processor(s) 301) and comprise information obtained by the muon detector that allows a trajectory of a charged particle to be estimated. Block 314 is similar to block 114 described above in relation to method 100 of FIG. 3 and trajectory data 312 and timing data 313 are similar to trajectory data 112 and timing data 113 described above in relation to method 100 of FIG. 3. Unless expressly indicated otherwise, the characteristics of block 114 and of trajectory data 112 and timing data 113 described herein apply to block 314 and to trajectory data 312 and timing data 313.

[0214] Sub-routine 310 then proceeds to block 318 which comprises obtaining deposited energy data 316 (energy data 316, for brevity) from the muon detector for the corresponding detection event. Energy data 316 may be generated by the muon detector (including any suitably connected and configured processor(s) 301). Energy data 316 of a detection event is associated with trajectory data 312 and optional timing data 313 of the same detection event - that is, each detection event may have an associated trajectory 312, optional timing data 313 and associated energy data 316. In some embodiments, energy data 316 comprises a measurement correlated with energy deposited by a particle as it interacts with the muon detector. Block 318 is similar to block 118 described in relation to method 100 of FIG. 3 and energy data 316 is similar to energy data 116 described above in relation to method 100 of FIG. 3. Unless expressly indicated otherwise, the characteristics of block 318 and of energy data 116 described herein apply to block 318 and to energy data 316.

[0215] Sub-routine 310 then proceeds to block 328 which comprises determining T-E discriminant 326 for the corresponding detection event. In some embodiments, T-E discriminant value 326 is a scalar value, although this is not necessary. In some embodiments, depending on the construction of the T-E discriminant determination model used in block 328), each T-E discriminant value 326 may comprise a vector. T-E discriminant value 326 may be determined based on input comprising trajectory data 312, energy data 316 and optional timing data 313 and may comprise anysuitable computational parameter based on a computational transformation of input comprising trajectory data 312, energy data 316 and optional timing data 313. As described elsewhere herein, there are scenarios where multiple beta particles may enter the muon detector at different positions such that their collective interactions mimic the energy deposition signature (sometimes including path-length-adjusted energy deposition signature and / or PLAA signature) of a muon particle traversing the detector. Consequently, there may be advantages to incorporating optional timing data 313 into T-E discriminant 326 such that T-E discriminant 326 is also effective at filtering the “multi-beta” false-positive tracks. As described in more detail elsewhere herein, T-E discriminant value 326 facilitates filtering of the measured muon data by a suitable filtering technique. PLAA energy data 126 described herein in relation to method 100 of FIG. 3 is a non-limiting example of a T-E discriminant value 326 and the processes of blocks 124 and 128 (FIG. 3) may represent a particular non-limiting example embodiment of the block 328 process of determining T-E discriminant value 326. In some embodiments, the block 328 process of determining T-E discriminant value 326 comprises inferring T-E discriminant value 326 using a machine-learning model which has been trained to generate T-E discriminant value 326 based on input comprising trajectory data 312, energy data 316, and optional timing data 313 and T-E discriminant value 326 comprises the inferred output of such a suitably trained machine-learning model.

[0216] T-E discriminant value 326 may be determined in block 328 by any suitable technique. In the non-limiting example embodiment of T-E discriminant value 326 being PLAA energy data 126 described elsewhere herein, the block 328 process of determining T-E discriminant 326 (PLAA energy data 126) comprises (i) adjusting (e.g. normalizing) energy data 316 for a particular detection event based on a path length of the estimated trajectory provided by trajectory data 312 (e.g. as described above in connection with block 124); and, (ii) optionally further adjusting (e.g. normalizing) energy data 316 based on an optional attenuation parameter correlated with energy attenuation in the muon detector (e.g. as described above in connection with block 128).

[0217] In some embodiments, the block 328 process of determining T-E discriminant value 326 comprises inferring T-E discriminant value 326 using a machine-learning model which has been trained to generate T-E discriminant value 326 based on input comprising trajectory data 312, energy data 316 and optionaltiming data 313 and T-E discriminant value 326 comprises the inferred output of such a suitably trained machine-learning model. The machine learning model used in block 328 may generally comprise any suitable machine learning model(s) with any suitable machine learning architecture(s) and any suitable set of trainable parameters. By way of non-limiting example, in a non-limiting example embodiment where the block 328 machine learning model comprises a neural network, the trainable parameters of the machine learning model may comprise the weights and / or biases of perceptrons of the neural network or otherwise associated with connections between nodes of the neural network.

[0218] In some embodiments, the machine learning model is trained to optimize the block 328 process of determining (e.g. inferring) T-E discriminant 326. Training the block 328 machine learning model may comprise using one or more sets of labelled detection event training data. Each set of labelled detection event training data may comprise a subset of labelled muon detection training data corresponding to a plurality of detection events associated with a population of muon particles (or an overwhelming majority of muon particles) and a subset of labelled beta detection training data corresponding to a plurality of detection events associated with a population of beta particles (or an overwhelming majority of beta particles). For example, the labelled detection event training data may comprise a plurality of detection events, each detection event comprising trajectory data 312, energy data 316 and optional timing data 313 and each detection event labelled as a muon event or a beta particle event; a set of labelled detection event data (e.g. training data set 408 used in a particular training iteration of subroutine 450 as described elsewhere herein) may comprise a subset of detection events labelled as muon events and a subset of detection events labelled as beta particle events. Such labelled detection event training data may be procured using the same muon detector (or the same type of muon detector) for which method 300 is being performed by detecting detection events in controlled environment(s), where detection events have a significantly higher likelihood of being a muon event (as compared to a beta particle event) or a significantly higher likelihood of being a beta particle event (as compared to a muon event).

[0219] In some embodiments, training the block 328 machine learning model to generate T-E discriminant 326 comprises performing an iterative training method. FIG. 6 is a schematic flowchart of a method 400 for iterative training of a machinelearning model 430 suitable for use in block 328 according to an example embodiment. Method 400 may be performed by any suitable processing unit(s) or cluster of processing unit(s).

[0220] Method 400 begins with block 402 which comprises postulating a T-E discriminant determination model 404 comprising arbitrary values for its trainable parameters. In some embodiments, the block 402 process of postulating T-E discriminant determination model 404 comprises generating random initial values for the trainable parameters of T-E discriminant determination model 404. In some embodiments, the block 402 process of postulating T-E discriminant determination model 404 comprises generating estimated initial values for the trainable parameters of T-E discriminant determination model 404 (e.g. estimated values based on prior performance(s) of method 400).

[0221] Method 400 then enters sub-routine 450. Sub-routine 450 begins with block 406 which comprises attempting to infer T-E discriminant values 412 using the current postulated T-E discriminant determination model (i.e. with the current trainable parameter values) using a set of training data 408 as input. In the first iteration of sub-routine 450, the current postulated T-E discriminant determination model used in block 406 may comprise model 404 postulated in block 402 (i.e. with initial values for its trainable parameters). In the second and subsequent iterations of sub-routine 450 (as described in more detail below), the current postulated T-E discriminant determination model used in block 406 may comprise modified model 404’ determined in block 428 (i.e. with updated trainable parameter values).

[0222] Training data set 408 used in each iteration of subroutine 450 may comprise a set of training data drawn (e.g. randomly drawn) from a larger collection of labelled detection event training data (not shown in Figure 6). As discussed above, the larger collection of labelled detection event training data may comprise a plurality of detection events, where each detection event comprises trajectory data 312, energy data 316, and optional timing data 313 and each detection event is labelled as a muon event or a beta particle event. Training data set 408 used in each iteration of sub-routine 450 may be drawn (e.g. randomly drawn) from this larger collection of labelled detection event training data and may comprise a subset of detection events labelled as muon events and a subset of detection events labelled as beta particle events.

[0223] Determining T-E discriminant values 412 based on training data set 408 inblock 406 comprises determining (e.g. inferring), for each detection event in training data set 408, a T-E discriminant value 412 based on (e.g. using) the current T-E discriminant determination model 404, 404’ to thereby obtain a set of determined T-E discriminant values 412 associated with the set of detection events in training data set 408. In some embodiments, each T-E discriminant value 412 is a scalar. This is not necessary, however, and, depending on the construction of T-E discriminant determination model 404, 404’, each T-E discriminant value 412 may comprise a vector. Because training data set 408 comprises a plurality of detection events and the block 406 process of determining T-E discriminant values 412 determines a T-E discriminant value for each detection event, the T-E discriminant values 412 output from the block 406 process comprises a distribution of T-E discriminant values.

[0224] Sub-routine 450 then proceeds to block 410 which comprises determining a T-E discriminant separation parameter 416 based on T-E discriminant values 412. In some embodiments, separation parameter 416 comprise a scalar T-E cut-off value (e.g. analogous to cut-off PLAA value 164 discussed above) by which the distribution of T-E discriminant values 412 can be filtered or otherwise separated. In some embodiments (e.g. where T-E discriminant values 412 comprise vector quantities), T-E discriminant separation parameter 416 may comprise a multi-dimensional vector.

[0225] In some embodiments, the block 410 process of determining T-E discriminant separation parameter 416 comprises determining an optimal T-E discriminant separation parameter 416 using an optimization algorithm (e.g. analogous to sub-routine 150 discussed above). Such an optimization algorithm may be based on a cost function which may comprise term(s) that assign cost to T-E discriminant separation parameter 416 that would result in the inclusion of beta particle detection events in what would otherwise be considered to be muon detection event data and / or that would result in the exclusion of muon detection events from what would otherwise be considered to be muon detection event data. In some embodiments, the determination of an optimal separation parameter 416 in block 410 may be subject to additional constraints, including, but not limited to imposing a limitation on complexity of optimal separation parameter 416, applying suitable regularization techniques, and / or the like.

[0226] In some embodiments, the block 410 process of determining a T-E discriminant separation parameter 416 may be analogous to the process of determining a cut-off PLAA value 164 discussed elsewhere herein (e.g. in connectionwith blocks 134, 136, 150, 152, 154 of method 100 - Figure 3) except that T-E discriminant values are used in the place of PLAA values and the distribution of inferred T-E discriminant values 412 may be used in the place of measured distribution 130 of PLAA energy data 126. Baseline distributions used for curve-fitting (analogous to baseline distributions 132 discussed in connection with method 100) may be obtained from the labelled training data set 408 (or from a different subset of the larger collection of labelled detection event training data). The T-E discriminant data for such baseline distributions maybe obtained using the current values of the trainable parameters of T-E discriminant determination model 404, 404’ or may be obtained using models obtained using a T-E discriminant determination model generated in a previous implementation of method 400.

[0227] Sub-routine 450 then proceeds to block 414 which comprises determining a separation evaluation score 420 for the current T-E discriminant determination model 404, 404’ (e.g. the current values of the trainable parameters). In some embodiments, determining evaluation score 420 in block 414 comprises the two-step process of: applying T-E discriminant separation parameter 416 to training data set 408 to filter (e.g. separate) the detection events of training data set 408 into one group of detection events considered to be predominantly muon detection events (the “retained” or “kept” subset of detection events) and a second group of detection events considered to be predominantly beta particle events (the “rejected” subset of detection events); and determining at least one of: an efficiency of separation; and, a purity of separation. Applying the T-E discriminant separation parameter 416 in block 414 may be analogous to the filtering procedure of block 166 (Figure 3) described herein, except that except that T-E discriminant values are used in the place of PLAA values and T-E discriminant separation parameter 416 is used in the place of cut-off PLAA value 164.

[0228] Determining the efficiency of separation may be based on a ratio of a number of muon detection events retained (after the filtering / separation step of block 414) in the retained group considered to be predominantly muon detection events to a total number muon detection events in training data set 408 (as known from the labels of training data set 408). Determining the purity of separation may be based on a ratio of a number of muon detection events (as known from the labels of training data set 408) retained (after filtering / separation) in the retained group considered to be predominantly muon detection events to a total number of detection events retained(after filtering / separation) in the retained group considered to be predominantly muon detection events. It will be appreciated by those skilled in the art that the efficiency of separation and purity of separation may additionally or alternatively be based on the group of detection events in training data set 408 that is rejected (after the filtering / separation step of block 414) - i.e. in the group considered to be predominantly beta particle detection events. For example, the efficiency of separation may be based on a ratio of a number of beta particle detection events rejected (after filtering / separation) in the group considered to be predominantly beta particle detection events to a total number beta particle detection events in training data set 408 (as known from the labels of training data set 408). Similarly, the purity of separation may be based on a ratio of a number of beta particle detection events (as known from the labels of training data set 408) rejected (after filtering / separation) in the group considered to be predominantly beta particle detection events to a total number of detection events rejected (after filtering / separation) in the group considered to be predominantly beta particle detection events. Evaluation score 420 for the current T-E discriminant determination model 404, 404’ may be stored in a suitable computer-readable memory medium.

[0229] Method 400 then proceeds to block 426 which comprises evaluating whether condition(s) for concluding the training of T-E discriminant determination model 404, 404’ have been met. The block 426 training conclusion condition(s) may comprise any suitable set of one or more conditions. In some embodiments, at least a component of the block 426 training conclusion condition(s) comprises evaluating whether one or more of previously determined evaluation scores 420 have exceeded a threshold score for concluding training. In some embodiments, at least a component of the block 426 training conclusion condition(s) comprises evaluating a probability (or likelihood) of further improving evaluation score 420 with further iterations of subroutine 450. For example, if the probability (or likelihood) of further improving evaluation score 420 with training is below a threshold probability or if the change in a number of successive evaluation scores 420 is below a threshold, then the method 400 training may be concluded. In some embodiments, at least a component of the block 426 training conclusion condition(s) comprises evaluating a trend of evaluation scores 420. For example, if evaluation score 420 has not improved by more than a threshold amount over a threshold number of training runs (e.g. sub-routine 450 iterations), then the method 400 training may be concluded. In some embodiments, atleast a component of the block 426 training conclusion condition(s) comprises whether the number of iterations of sub-routine 450 has exceeded a threshold. Any of the block 426 training conclusion conditions described herein may be combined.

[0230] If the block 426 inquiry determines that the training conclusion condition(s) have been met, then method 400 proceeds along “YES” branch to block 427, which involves outputting trained T-E discriminant model 430. Trained T-E discriminant model 430 output in block 427 may comprise T-E discriminant model 404, 404' associated with the iteration of sub-routine 450 which generates the highest evaluation score 420. Trained T-E discriminant model 430 output in block 427 may comprise T-E discriminant model 404, 404' associated with the last iteration of subroutine 450.

[0231] If the block 426 inquiry determines that the training conclusion condition(s) have not been met, then method 400 proceeds along “NO” branch to block 428 which comprises modifying the current T-E discriminant determination model (e.g. modifying the trainable parameters of the current T-E discriminant determination model) to generate modified T-E discriminant determination model 404’ (“modified model 404”’ herein for brevity).

[0232] In general, the block 428 process of modifying the current T-E discriminant determination model to provide modified model 404’ may comprise modifying the current T-E discriminant determination model in any suitable manner by any suitable techniques. For example, if the T-E discriminant determination model comprises a neural network, then modifying the current T-E discriminant may comprise updating trainable parameters (e.g. weights and / or biases) of the neural network via back propagation. In some embodiments, the block 428 process of modifying the current T-E discriminant determination model (e.g. the values of the trainable parameters of the current T-E discriminant determination model) is based, at least in part, on the evaluation score 420. After generating modified model 404’, method 400 loops back to perform another iteration of sub-routine 450 which now operates on modified model 404’ (e.g. in the place of originally postulated model 404). Method 400 then iterates sub-routine 450 until the block 426 training conclusion condition(s) have been met, resulting in the output of trained T-E discrimination model 430 in block 427. As discussed above, trained T-E discrimination model 430 may be used in block 328 of method 300 (FIG. 5) to generate a T-E discriminant value 326 for each detection event.

[0233] Returning to FIG. 5, after completing sub-routine 310 for each detection event in a plurality of detection events, the T-E discriminant values 326 for the plurality of detection events are collected to form a measured distribution of T-E discriminant values 330. Measured distribution of T-E discriminant values 330 may be analogous to (and share analogous feature of) measured PLAA distribution 130 discussed above, except that measured PLAA distribution 130 provides a distribution of PLAA values (which is one example of a suitable T-E discriminant value), whereas measured distribution of T-E discriminant values 330 provides a distribution of any suitable T-E discriminant values.

[0234] Method 300 then proceeds to block 334 which comprises obtaining baseline distributions 332 and measured distribution 330. Baseline distributions 332 (as used herein) refer to distributions of T-E discriminant values established for corresponding particles (e.g. beta particles, muon particles, etc.) that reflect salient properties of the corresponding particles or salient relationships among the corresponding particles. Baseline distributions 332 may be analogous to baseline distributions 132 described herein, including example beta particle baseline distribution 132B and example muon baseline distribution 132M shown in Figures 4B and 4G, except that the abscissa of baseline distributions 332 would be in coordinates of T-E discriminant value rather than PLAA. In some embodiments, baseline distributions 332 are taken as an ansatz (e.g. based on first principle considerations). For example, both the T-E discriminant distribution for beta particles and the T-E discriminant distribution for muon particles may be assumed to be log-normally distributed and the mode for the T-E discriminant distribution for beta particles may be assumed to be some fraction (e.g. one half) of the mode of the T-E discriminant distribution for muon particles. In some embodiments, baseline distributions 332 are empirically derived for specific charged particles (e.g. muon particles, beta particles, etc.) through measurements in a controlled environment or within a defined subsample of T-E discriminant values such that each baseline distribution 332 of T-E discriminant values is primarily the result of a specific desired charged particle.

[0235] In some embodiments, baseline distributions 332 may be obtained by applying the block 328 T-E discriminant determination process to detection events known to correspond to specific charged particles (e.g. muon particles, beta particles, etc.). For example, the labelled detection event training data discussed above in the context of training method 400 comprises detection events labelled as muon eventsor beta events. A baseline beta particle distribution 332 may be obtained by applying the block 328 T-E discriminant determination process to a set of such training data known to correspond to beta particle detection events and a baseline muon distribution 332 may be obtained by applying the block 328 T-E discriminant determination process to a set of such training data known to correspond to muon detection events.

[0236] After obtaining baseline distributions 332, method 300 proceeds to block 336 which comprises fitting measured distribution 330 to baseline distributions 332 by any suitable fitting methodology. The block 336 curve-fitting process may be analogous to (and share characteristics with) the block 136 curve-fitting process described elsewhere herein. Block 336 may be based on the assumption that measured T-E discriminant distribution 330 is a result of contribution from both baseline beta particle distribution and baseline muon particle distribution and, that, consequently, measured T-E discriminant distribution 330 can be estimated as a combination of baseline beta particle distribution and baseline muon particle distribution.

[0237] Block 336 may comprise any suitable curve fitting technique comprising any suitable set of curve-fitting parameters. The output of the block 336 curve-fitting process may be a set of curve-fitting parameter values 340. In a non-limiting example embodiment, curve-fitting parameters 340 comprise a first constant multiplier for baseline beta particle distribution 332 and a second constant multiplier for baseline muon particle distribution 332.

[0238] Method 300 then proceeds to a sub-routine 350 for filtering noise from data 312 obtained by the muon detector to generate noise-filtered trajectory data 370. Sub-routine 350 may be analogous to (and share characteristics with) the sub-routine 150 described elsewhere herein. In the particular case of the illustrated embodiment, sub-routine 350 comprises: determining a T-E discriminant separation parameter 364; and filtering measured T-E discriminant distribution 330 by removing, from consideration, a rejection subset of detection events associated with T-E discriminant values designated for removal by T-E discriminant separation parameter 364 (e.g. considered to be beta particles) to arrive at noise-filtered trajectory data 370 - i.e. a retained subset of detection events considered to correspond to muon events. In some embodiments, T-E discriminant separation parameter 364 comprises applying a T-E discriminant cut-off value to measured distribution 330 in a manner analogous tothe application of cut-off PLAA value 164 to measured distribution 130 discussed above and analogous to the application of T-E discriminant separation parameter 416 discussed above in connection with block 414.

[0239] In some embodiments, detection events in measured T-E discriminant distribution 330 that are at least n standard deviations away from the mean of fitted baseline muon particle distribution and / or within m standard deviations of fitted baseline beta particle distribution may be identified as beta particle detection events and subsequently removed (filtered) from trajectory data 312 to obtain noise-filtered trajectory data 370, as described below. The parameters n, m can be any number greater than zero. As discussed below, as compared to the measured data prior to filtering (e.g. measured T-E discriminant distribution 330), noise-filtered trajectory data 370 (i.e. the retained set of detection events) will have a relatively high fraction of detection events corresponding to muons and a relatively low fraction of detection events corresponding to beta particles.

[0240] Sub-routine 350 of the illustrated embodiment begins with block 352 which involves generating a cost function which may be used for determining an optimal T-E discriminant separation parameter 364. The block 352 cost function may comprise a function of T-E discriminant value (as the variable) and may be parameterized at least by curve-fitting parameter values 340. The block 352 cost function may have terms that assign cost to: undesirably retaining (e.g. in the retained subset) detection events that may be results of beta energy deposition; and, undesirably filtering (i.e. removing or placing in the rejection subset) detection events that may be results of muon energy deposition.

[0241] Sub-routine 350 then proceeds to block 354, which involves determining an optimal T-E discriminant separation parameter 364. In some embodiments, block 354 comprises selecting a T-E discriminant separation parameter 364 that minimizes the block 352 cost function. Block 366 then uses the block 354 T-E discriminant separation parameter 364 to filter the measured trajectory data 312 (e.g. detection events) and to thereby obtain noise-filtered trajectory data 370 corresponding to the retained subset of detection events.

[0242] In some embodiments, trajectory data 312 is additionally or alternatively filtered on the basis of timing data 313 at block 366. Additional filtering based on timing data 313 at block 366 may be particularly advantageous if timing data 313 is not already incorporated into T-E discriminant 326. Timing data 313 is similar totiming data 113 described elsewhere herein, and the application of timing data 313 at block 366 for further filtering of trajectory data 312 is similar to the application of timing data 113 at block 166. Unless expressly indicated otherwise, the characteristics of block 166 in relation to timing data 113 described herein apply to block 366 in relation to timing data 313.

[0243] Other additional or alternative filtering technique(s) may also be applied at block 366. For example, for muon detectors deployed underground, most muons are expected to arrive at the muon detectors from a side of the muon detector closer to the surface of the earth, whereas particles arriving at the muon detectors from below the detector (i.e. a side of the detector further from the surface of the earth) are somewhat more likely to be beta particles due to the presence of beta particle sources in earth. Consequently, in regions of the measured T-E discriminant distribution 330 where fitted baseline muon particle distribution and fitted baseline beta particle distribution overlap, trajectory data 312 may be additionally or alternatively filtered on the basis of the orientation of the trajectory (i.e. the location of the entry and exit points of the given trajectory through the muon detector).

[0244] FIG. 7 is a schematic flowchart of a method 500 for filtering noise in trajectory data obtained by muon detectors according to another example embodiment. Method 500 can be applied to filter noise in any suitable muon detectors, including, but not limited to, muon detectors comprising sub-detector elements sensitive to charged particles (e.g. scintillator elements). While the methods and systems described herein are particularly suitable for borehole muon detectors deployed underground (e.g. the borehole muon detectors of FIGs. 1A, 1 B), unless expressly indicated, the methods and systems described herein are not limited to any particular type of muon detector or to any particular application of a muon detector.

[0245] Method 500 may be performed by one or more suitably configured processor(s) 501. Processor(s) 501 may be embedded in a muon detector (e.g. one of muon detectors 10A, 10B described above, although that is not necessary) or operatively coupled to, e.g. in data communication with, one or more muon detectors to receive data therefrom. Method 500 may begin with a sub-routine 510. In some embodiments, sub-routine 510 is performed for each detection event.

[0246] For a given detection event, sub-routine 510 begins with block 514 which involves obtaining trajectory data 512 and optional timing data 513 for the corresponding detection event. Trajectory data 512 and optional timing data 513 maybe generated by the muon detector (including any suitably connected and configured processor(s) 501) and comprise information obtained by the muon detector that allows a trajectory of a charged particle to be estimated. Block 514 is similar to block 114 described above in relation to method 100 of FIG. 3 and trajectory data 512 and timing data 513 are similar to trajectory data 112 and timing data 113 described above in relation to method 100 of FIG. 3. Unless expressly indicated otherwise, the characteristics of block 114 and of trajectory data 112 and timing data 113 described herein apply to block 514 and to trajectory data 512 and timing data 513.

[0247] Sub-routine 510 then proceeds to block 518 which comprises obtaining deposited energy data 516 (energy data 516, for brevity) from the muon detector for the corresponding detection event. Energy data 516 may be generated by the muon detector (including any suitably connected and configured processor(s) 501). Energy data 516 of a detection event is associated with trajectory data 512 and optional timing data 513 of the same detection event - that is, each detection event may have an associated trajectory 512, associated optional timing 513 and associated energy data 516. In some embodiments, energy data 516 comprises a measurement correlated with energy deposited by a particle as it interacts with the muon detector. Block 518 is similar to block 118 described in relation to method 100 of FIG. 3 and energy data 516 is similar to energy data 116 described above in relation to method 100 of FIG. 3. Unless expressly indicated otherwise, the characteristics of block 318 and of energy data 116 described herein apply to block 518 and to energy data 516.

[0248] Sub-routine 510 is then concluded and generates a collection of combined detection event data 532 in association of the plurality of detection events identified by the detector - i.e. each detection event data comprises corresponding trajectory data 512, energy data 516, and optional timing data 513. As described elsewhere herein, there are scenarios where multiple beta particles may enter the muon detector at different positions such that their collective interactions mimic the energy deposition signature (sometimes including path-length-adjusted energy deposition signature and / or PLAA signature) of a muon particle traversing the detector.Consequently, there may be advantages to incorporating optional timing data 313 into combined detection event data 532 to enable more effective filtering of the “multibeta” false-positive tracks. Method 500 then proceeds to block 528 which comprises providing collection of combined detection event data 532 as inputs to a machine learning model. The block 528 machine learning model may comprise any suitablemachine learning model(s) with any suitable architectures. For example, in a nonlimiting example embodiment where the block 528 machine learning model comprises a neural network, the trainable parameters of the block 528 machine learning model comprise weights and / or biases associated with perceptrons of the neural network or otherwise associated with connections between nodes of the neural network. The block 528 machine learning algorithm may be trained to assign, as an output, a probability value 564 to each detection event based on the corresponding energy data 516 and trajectory data 512 of the detection event. The outputted probability value 564 for each detection event reflects the probability of the corresponding detection event being a muon detection event (as opposed to a detection event caused by a beta particle or other particle).

[0249] Method 500 then proceeds to block 566 which comprises filtering or weighting trajectory data 512 to generate noise-filtered trajectory data 570 based at least on the plurality of probability values 564 outputted by the machine learning algorithm. In some embodiments, filtering trajectory data 512 based on the plurality of probability values 564 comprises determining, for each detection event, whether the corresponding probability value 564 is above a probability threshold.

[0250] Where a component (e.g. a software module, processor, assembly, device, circuit, etc.) is referred to herein, unless otherwise indicated, reference to that component (including a reference to a “means”) should be interpreted as including as equivalents of that component any component which performs the function of the described component (i.e. , that is functionally equivalent), including components which are not structurally equivalent to the disclosed structure which performs the function in the illustrated exemplary embodiments of the invention.

[0251] Embodiments of the invention may be implemented using specifically designed hardware, configurable hardware, programmable data processors configured by the provision of software (which may optionally comprise “firmware”) capable of executing on the data processors, special purpose computers or data processors that are specifically programmed, configured, or constructed to perform one or more steps in a method as explained in detail herein and / or combinations of two or more of these. Examples of specifically designed hardware are: logic circuits, application-specific integrated circuits (“ASICs”), large scale integrated circuits (“LSIs”), very large scale integrated circuits (“VLSIs”), and the like. Examples of configurable hardware are: one or more programmable logic devices such asprogrammable array logic (“PALs”), programmable logic arrays (“PLAs”), and field programmable gate arrays (“FPGAs”). Examples of programmable data processors are: microprocessors, digital signal processors (“DSPs”), embedded processors, graphics processors, math co-processors, general purpose computers, server computers, cloud computers, mainframe computers, computer workstations, and the like. For example, one or more data processors in a control circuit for a device may implement methods as described herein by executing software instructions in a program memory accessible to the processors.

[0252] Processing may be centralized or distributed. Where processing is distributed, information including software and / or data may be kept centrally or distributed. Such information may be exchanged between different functional units by way of a communications network, such as a Local Area Network (LAN), Wide Area Network (WAN), or the Internet, wired or wireless data links, electromagnetic signals, or other data communication channel.

[0253] The invention may also be provided in the form of a program product. The program product may comprise any non-transitory medium which carries a set of computer-readable instructions which, when executed by a data processor, cause the data processor to execute a method of the invention. Program products according to the invention may be in any of a wide variety of forms. The program product may comprise, for example, non-transitory media such as magnetic data storage media including floppy diskettes, hard disk drives, optical data storage media including CD ROMs, DVDs, electronic data storage media including ROMs, flash RAM, EPROMs, hardwired or preprogrammed chips (e.g., EEPROM semiconductor chips), nanotechnology memory, or the like. The computer-readable signals on the program product may optionally be compressed or encrypted.

[0254] In some embodiments, the invention may be implemented in software. For greater clarity, “software” includes any instructions executed on a processor, and may include (but is not limited to) firmware, resident software, microcode, code for configuring a configurable logic circuit, applications, apps, and the like. Both processing hardware and software may be centralized or distributed (or a combination thereof), in whole or in part, as known to those skilled in the art. For example, software and other modules may be accessible via local memory, via a network, via a browser or other application in a distributed computing context, or via other means suitable for the purposes described above.

[0255] Software and other modules may reside on servers, workstations, personal computers, tablet computers, and other devices suitable for the purposes described herein.Interpretation of Terms

[0256] Unless the context clearly requires otherwise, throughout the description and the claims:• “comprise”, “comprising”, and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”;• “connected”, “coupled”, or any variant thereof, means any connection or coupling, either direct or indirect, between two or more elements; the coupling or connection between the elements can be physical, logical, or a combination thereof;• “herein”, “above”, “below”, and words of similar import, when used to describe this specification, shall refer to this specification as a whole, and not to any particular portions of this specification;• “or”, in reference to a list of two or more items, covers all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list;• the singular forms “a”, “an”, and “the” also include the meaning of any appropriate plural forms. These terms (“a”, “an”, and “the”) mean one or more unless stated otherwise;• “and / or” is used to indicate one or both stated cases may occur, for example A and / or B includes both (A and B) and (A or B);• “approximately” when applied to a numerical value means the numerical value ± 10%;• where a feature is described as being “optional” or “optionally” present or described as being present “in some embodiments” it is intended that the present disclosure encompasses embodiments where that feature is present and other embodiments where that feature is not necessarily present and other embodiments where that feature is excluded. Further, where any combination of features is described in this application this statement is intended to serve as antecedent basis for the use of exclusive terminologysuch as "solely," "only" and the like in relation to the combination of features as well as the use of "negative" limitation(s)” to exclude the presence of other features; and• “first” and “second” are used for descriptive purposes and cannot be understood as indicating or implying relative importance or indicating the number of indicated technical features.

[0257] Words that indicate directions such as “vertical”, “transverse”, “horizontal”, “upward”, “downward”, “forward”, “backward”, “inward”, “outward”, “left”, “right”, “front”, “back”, “top”, “bottom”, “below”, “above”, “under”, and the like, used in this description and any accompanying claims (where present), depend on the specific orientation of the apparatus described and illustrated. The subject matter described herein may assume various alternative orientations. Accordingly, these directional terms are not strictly defined and should not be interpreted narrowly.

[0258] Where a range for a value is stated, the stated range includes all subranges of the range. It is intended that the statement of a range supports the value being at an endpoint of the range as well as at any intervening value to the tenth of the unit of the lower limit of the range, as well as any subrange or sets of sub ranges of the range unless the context clearly dictates otherwise or any portion(s) of the stated range is specifically excluded. Where the stated range includes one or both endpoints of the range, ranges excluding either or both of those included endpoints are also included in the invention.

[0259] Certain numerical values described herein are preceded by "about". In this context, "about" provides literal support for the exact numerical value that it precedes, the exact numerical value ±5%, as well as all other numerical values that are near to or approximately equal to that numerical value. Unless otherwise indicated a particular numerical value is included in “about” a specifically recited numerical value where the particular numerical value provides the substantial equivalent of the specifically recited numerical value in the context in which the specifically recited numerical value is presented. For example, a statement that something has the numerical value of “about 10” is to be interpreted as: the set of statements:• in some embodiments the numerical value is 10;• in some embodiments the numerical value is in the range of 9.5 to 10.5; and if from the context the person of ordinary skill in the art would understand that values within a certain range are substantially equivalent to 10 because the valueswith the range would be understood to provide substantially the same result as the value 10 then “about 10” also includes:• in some embodiments the numerical value is in the range of C to D where C and D are respectively lower and upper endpoints of the range that encompasses all of those values that provide a substantial equivalent to the value 10

[0260] Specific examples of systems, methods and apparatus have been described herein for purposes of illustration. These are only examples. The technology provided herein can be applied to systems other than the example systems described above. Many alterations, modifications, additions, omissions, and permutations are possible within the practice of this invention. This invention includes variations on described embodiments that would be apparent to the skilled addressee, including variations obtained by: replacing features, elements and / or acts with equivalent features, elements and / or acts; mixing and matching of features, elements and / or acts from different embodiments; combining features, elements and / or acts from embodiments as described herein with features, elements and / or acts of other technology; and / or omitting combining features, elements and / or acts from described embodiments.

[0261] As will be apparent to those of skill in the art upon reading this disclosure, each of the individual embodiments described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any other described embodiment(s) without departing from the scope of the present invention.

[0262] Any aspects described above in reference to apparatus may also apply to methods and vice versa.

[0263] Any recited method can be carried out in the order of events recited or in any other order which is logically possible. For example, while processes or blocks are presented in a given order, alternative examples may perform routines having steps, or employ systems having blocks, in a different order, and some processes or blocks may be deleted, moved, added, subdivided, combined, and / or modified to provide alternative or subcombinations. Each of these processes or blocks may be implemented in a variety of different ways. Also, while processes or blocks are at times shown as being performed in series, these processes or blocks may instead be performed in parallel, simultaneously or at different times.

[0264] Various features are described herein as being present in “some embodiments”. Such features are not mandatory and may not be present in all embodiments. Embodiments of the invention may include zero, any one or any combination of two or more of such features. All possible combinations of such features are contemplated by this disclosure even where such features are shown in different drawings and / or described in different sections or paragraphs. This is limited only to the extent that certain ones of such features are incompatible with other ones of such features in the sense that it would be impossible for a person of ordinary skill in the art to construct a practical embodiment that combines such incompatible features. Consequently, the description that “some embodiments” possess feature A and “some embodiments” possess feature B should be interpreted as an express indication that the inventors also contemplate embodiments which combine features A and B (unless the description states otherwise or features A and B are fundamentally incompatible).This is the case even if features A and B are illustrated in different drawings and / or mentioned in different paragraphs, sections or sentences.

[0265] It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions, omissions, and sub-combinations as may reasonably be inferred. The scope of the claims should not be limited by the preferred embodiments set forth in the examples, but should be given the broadest interpretation consistent with the description as a whole.

Claims

WHAT IS CLAIMED IS:

1. A method for filtering noise from measured data obtained by a muon detector, the method comprising:obtaining a measured distribution of path-length-adjusted energy data for a plurality of detection events associated with the measured data, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the path-length- adjusted energy data is representative of energy deposited by the corresponding particle per unit path length in the detector;fitting the measured distribution to first and second baseline distributions of deposition energy per unit path length wherein:the first baseline distribution of deposition energy per unit path length is obtained from a first baseline environment with a high concentration of muon particles relative to beta particles;the second baseline distribution of deposition energy per path length is obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and,filtering the measured data obtained by the detector based at least on the determined distribution fitting parameters to thereby obtain noise-filtered measured data.

2. The method of claim 1 or any other claim herein wherein obtaining the measured distribution comprises, for each detection event, obtaining (e.g. measuring) an energy measurement representative of energy deposited by the corresponding particle in the detector.

3. The method of claim 2 or any other claim herein wherein obtaining the measured distribution comprises, for each detection event: determining a path length associated with a trajectory of the corresponding particle through the detector; and determining the path-length-adjusted energy data for thecorresponding particle by normalizing the energy measurement based on the path length.

4. The method of claim 3 or any other claim herein wherein determining path length associated with a trajectory of the corresponding particle through the detector comprises determining a trajectory of the corresponding particle through the detector.

5. The method of claim 4 or any other claim herein wherein determining the trajectory of the corresponding particle through the detector is based on the measured data obtained by the detector.

6. The method of any one of claims 4 to 5 or any other claim herein wherein determining the trajectory of the corresponding particle through the detector comprises determining two three-dimensional locations where the charged particle interacted with the detector.

7. The method of claim 6 or any other claim herein wherein determining the two three-dimensional locations where the charged particle interacted with the detector is based on the measured data obtained by the detector.8 The method of any one of claims 1 to 7 or any other claim herein wherein obtaining the measured distribution comprises, for each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

9. The method of clam 8 or any other claim herein wherein, for each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on the attenuation parameter comprises scaling (e.g. multiplying) the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

10. The method of any one of claims 8 to 9 or any other clam herein wherein, for each detection event, the attenuation parameter is based on an expectedenergy attenuation associated with interaction of the corresponding charged particle with the detector.

11. The method of claim 10 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a location where the corresponding charged particle interacts with the detector.

12. The method of claim 11 or any other claim herein comprising, for each detection event, determining the location where the corresponding charged particle interacts with the detector is based on the measured data obtained by the detector.

13. The method of any one of claims 11 to 12 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

14. The method of claim 13 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a distance between the location where the corresponding charged particle interacts with the detector and the location of the sensor.

15. The method of any one of claims 8 to 9 or any other clam herein wherein, for each detection event, the attenuation parameter is based on a distance between a location where the corresponding charged particle interacts with the detector and a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

16. The method of any one of claims 1 to 15 or any other claim herein wherein the first baseline environment has a high concentration (e.g. flux) of muon particles relative to a concentration (e.g. flux) of beta particles.

17. The method of any one of claims 1 to 16 or any other claim herein wherein thesecond baseline environment has a high concentration (e.g. flux) of beta particles relative to a concentration (e.g. flux) of muon particles.

18. The method of any one of claims 1 to 16 or any other claim herein wherein the muon detector used to obtain the measured distribution is of the same type of muon detector used to obtain the first and second baseline distributions.

19. The method of any one of claims 1 to 18 or any other claim herein wherein filtering the measured data obtained by the detector comprises determining a cut-off path-length-adjusted energy value.

20. The method of claim 19 or any other claim herein wherein filtering the measured data obtained by the detector comprises: keeping, in the noise- filtered measured data, detection events with path-length-adjusted energy values greater than the cut-off path-length-adjusted energy value; and rejecting, from the noise-filtered measured data, detection events with path- length-adjusted energy values less than the cut-off path-length-adjusted energy value.

21. The method of any one of claims 19 to 20 or any other claim herein wherein determining the cut-off path-length-adjusted energy value comprises minimizing a cost function parameterized by the plurality of distribution fitting parameters.

22. The method of claim 21 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector.

23. The method of any one of claims 21 to 22 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events within the plurality ofdetection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

24. The method of any one of claims 21 to 23 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the fitting of the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of a muon particle with the detector.

25. The method of any one of claims 21 to 24 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

26. The method of any one of claims 1 to 25 or any other claim herein wherein the plurality of distribution fitting parameters comprises, for each of the first and second based line distributions, one or more of: a peak location parameter, an amplitude scaling parameter and a variance scaling parameter.

27. The method of any one of claims 1 to 26 or any other claim herein comprising obtaining timing data associated with the measured data of each detection event and filtering the measured data based on the timing data, wherein the timing data for each detection event comprises information indicative of an estimated transit time of a charged particle through the muon detector.

28. The method of claim 27 or any other claim herein wherein filtering the measured data based on the timing data comprises, for each detection event, determining an expected time range based at least on a path length of the path of the measured trajectory data and comparing the estimated transit time to the expected time range.

29. The method of claim 28 or any other claim herein wherein comparing the estimated transit time to the expected time range comprises excluding detection events with transit time outside the expected time range from the noise-filtered measured data and keeping detection events with transit time within the expected time range in the noise-filtered measured data.

30. The method of claim 27 or any other claim herein filtering the measured data based on the timing data comprises, for each detection event, calculating a particle speed based on the timing data and determining an acceptance range of an expected speed of muons based on the trajectory data and excluding detection events with calculated particle speed outside the acceptance range of the expected speed of muons and keeping detection events with calculated particle speed within the acceptance range of the expected speed of muons.

31. The method of any one of claims 27 to 30 or any other claim herein wherein the timing data for each detection event comprises at least a first time component of a first spatiotemporal point corresponding to a point of entry in the detection event and a second time component of a second spatiotemporal point corresponding to a point of exit in the detection event.

32. The method of claim 31 or any other claim herein wherein the estimated transit time of the charged particle for a given detection event is calculated as a difference between the first and second time components of the first and second spatiotemporal points.

33. An apparatus for filtering measured data obtained by a muon detector where the measured data comprises a plurality of detection events, each detection event associated with interaction of a corresponding charged particle with the muon detector, the apparatus comprising:an energy sensing system for determining, for each detection event, a measured energy deposited by the corresponding particle in the muon detector;a processor connected to the energy sensing system to receive, for each detection event, the measured energy, the processor configured to:determine a measured distribution of path-length-adjusted energy data for the plurality of detection events, wherein, for each detection event, the path-length-adjusted energy data is representative of energy deposited by the corresponding particle per unit path length in the detector;fit the measured distribution to first and second baseline distributions of deposition energy per unit path length wherein:the first baseline distribution of deposition energy per unit path length is obtained from a first baseline environment with a high concentration of muon particles relative to beta particles;the second baseline distribution of deposition energy per path length is obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; andfitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and,filter the measured data obtained by the detector based at least on the determined distribution fitting parameters to thereby obtain noise- filtered measured data.

34. An apparatus according to claim 33 comprising any of the features, combinations of features and / or sub-combinations of features of any of claims 1 to 26.

35. A method for filtering noise from measured data obtained by a muon detector, the method comprising:obtaining measured energy data and measured trajectory data for a plurality of detection events, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the measured energy data is representative of energy deposited by the corresponding charged particle in the detector and the measured trajectory data is representative of a path of the corresponding charged particle through the detector;determining, for each detection event, a T-E discriminant value based on the measured energy data and the measured trajectory data corresponding to the detection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality of detection events;fitting the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein:the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and,filtering the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise- filtered measured data.

36. The method of claim 35 or any other claim herein, wherein the T-E discriminant value comprises a scalar value.

37. The method of any one of claims 35 to 36 or any other claim herein, wherein filtering the measured data obtained by the detector comprises determining a cut-off T-E discriminant value.

38. The method of claim 37 or any other claim herein wherein filtering the measured data obtained by the detector comprises: keeping, in the noise- filtered measured data, detection events with T-E discriminant values that are one of greater than or less than the cut-off T-E discriminant value; and rejecting, from the noise-filtered measured data, detection events with T-E discriminant values that are the other one of greater than or less than the cutoff T-E discriminant value.

39. The method of claim 37 or 38 or any other claim herein wherein determining the cut-off T-E discriminant value comprises minimizing a cost function.

40. The method of claim 39 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector.

41. The method of claim 39 or 40 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

42. The method of any one of claims 39 to 41 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting, from the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of a muon particle with the detector.

43. The method of any one of claims 39 to 42 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting, from the noise-filtered measured data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

44. The method of any one of claims 35 to 43 or any other claim herein, wherein determining, for each detection event, the T-E discriminant value comprises applying a T-E discriminant determination model to the measured energy dataand the measured trajectory data corresponding to the detection event to thereby infer the T-E discriminant value for the detection event.

45. The method of claim 44 or any other claim herein wherein the T-E discriminant determination model comprises a machine-learning model comprising trainable parameters.46 The method of claim 45 or any other claim herein comprising training the machine-learning model, wherein training the machine-learning model comprises: initializing values for the trainable parameters; and performing a plurality of training iterations, each training iteration comprising:(i) determining, for each detection event in a set of labelled detection event training data, a T-E discriminant value based on current values for the trainable parameters of the T-E discriminant determination model to thereby obtain a corresponding distribution of T-E discriminant values;(ii) determining a T-E discriminant separation parameter for the corresponding distribution of T-E discriminant values, the T-E discriminant separation parameter indicative of which detection events in the corresponding distribution of T-E discriminant values should be retained as being likely muon events and which detection events in the corresponding distribution of T-E discriminant values should be rejected as being unlikely to be muon events;(iii) applying the T-E discriminant separation parameter to the corresponding distribution of T-E discriminant values to thereby obtain a retained subset of detection events from within the set of labelled detection event data determined by the T-E discriminant determination model as being likely muon events and a rejection subset of detection events from within the set of labelled detection event data determined by the T-E discriminant determination model as being unlikely to be muon events;(iv) determining an evaluation score associated with the current values of the trainable parameters of the T-E discriminant determination model based on labels associated with the set of labelled detection event training data and at least one of: the retained subset of detection events and the rejection subset of detection events; and(v) modifying the values of the trainable parameters of the T-E discriminantdetermination model.

47. The method of claim 46 or any other claim herein wherein, for each iteration, the set of labelled detection event training data comprises: a subset of labelled muon detection training data corresponding to a plurality of detection events associated with a population of muon particles and a subset of labelled beta detection training data corresponding to a plurality of detection events associated with a population of beta particles.

48. The method of any one of claims 46 to 47 or any other claim herein wherein, for each iteration, the set of labelled detection event training data comprises, for each of a plurality of training detection events: trajectory data, energy data and a label indicating the training detection event to be either a muon event or a beta particle event.

49. The method of any one of claims 46 to 48 or any other claim herein wherein, for each iteration, the set of labelled detection event training data is different from set of labelled detection event training data used in other iterations.

50. The method of any one of claims 46 to 49 or any other claim herein wherein, for each iteration, the set of labelled detection event training data is drawn from a larger collection of labelled detection event training data, wherein the larger collection of labelled detection event training data comprises, for each of a larger plurality of training detection events: trajectory data, energy data and a label indicating the event to be either a muon event or a beta particle event.

51. The method of claim 50 or any other claim herein wherein, for each iteration the set of labelled detection event training data is randomly drawn from the larger collection of labelled detection event training data.

52. The method of any one of claims 46 to 51 or any other claim herein wherein, for each iteration, determining the T-E discriminant separation parameter comprises determining optimizing a cost function to determine an optimal T-E discrimination separation parameter.

53. The method of claim 52 or any other claim herein wherein the cost function comprises one or more terms attributing cost to at least one of: retaining, in the retained subset, detection events from within the set of labelled detection event data labelled as beta particles or comprising beta particle labels; and rejecting, in the rejection subset, detection events from within the set of labelled detection event data labelled as muons or comprising muon labels.

54. The method of any one of claims 46 to 53 or any other claim herein wherein, for each iteration, determining the evaluation score comprises determining an efficiency of separation.

55. The method of claim 54 or any other claim herein wherein determining the efficiency of separation comprises at least one of:determining a ratio of a number of detection events in the retained subset that are labelled as muons or comprise muon labels to a total number detection events in the set of labelled detection evet training data that are labelled as muons or comprise muon labels; anddetermining a ratio of a number of detection events in the rejection subset that are labelled as beta particles or comprise beta particle labels to a total number detection events in the set of labelled detection evet training data that are labelled as beat particles or comprise beta particle labels.

56. The method of any one of claims 46 to 55 or any other claim herein wherein, for each iteration, determining the evaluation score comprises determining a purity of separation.

57. The method of claim 56 or any other claim herein wherein determining the purity of separation comprises at least one of:determining a ratio of a number of detection events in the retained subset that are labelled as muons or comprise muon labels to a total number of detection events in the retained subset; anddetermining a ratio of a number of detection events in the rejection subset that are labelled as beta particles or comprise beta particle labels to a totalnumber of detection events in the rejection subset.

58. The method of any one of claims 46 to 57 or any other claim herein wherein, for each iteration, modifying the values of the trainable parameters is based at least in part on the determined evaluation score.

59. The method of any one of claims 46 to 58 or any other claim herein wherein, for each iteration, modifying the values of the trainable parameters comprises implementing back propagation.

60. The method of any one of claims 46 to 59 or any other claim herein wherein each iteration further comprises evaluating one or more training conclusion conditions and, if the one or more training conclusion conditions are met: ceasing training of the machine-learning model; and determining the machinelearning model with the current values of the trainable parameters to be the T- E discriminant determination model.

61. The method of claim 60 or any other claim herein wherein the one or more training conclusion conditions comprise at least one of: one or more of previously determined evaluation scores exceeding a threshold score; a probability of further improving the evaluation score with further training iterations is below a threshold probability; a change in a number of successive evaluation scores is below a threshold change; the evaluation score has not improved by more than a threshold amount over a threshold number of training iterations; and a number of training iterations exceeding a threshold number.

62. The method of any one of claims 35 to 44 or any other claim herein wherein, for each detection event, the T-E discriminant value comprises a path-length- and-attenuation-adjusted (PLAA) energy value.

63. The method of any one of claims 35 to 44 or any other claim herein wherein, for each detection event, the T-E discriminant value comprises a path-length- adjusted energy data representative of energy deposited by the corresponding per unit path length in the detector.

64. The method of claim 63 or any other claim herein wherein obtaining the measured energy data comprises, for each detection event, obtaining (e.g. measuring) an energy measurement representative of energy deposited by the corresponding particle in the detector.

65. The method of claim 64 or any other claim herein wherein obtaining the measured energy data comprises, for each detection event: determining a path length associated with a trajectory of the corresponding particle through the detector; and determining the path-length-adjusted energy data for the corresponding particle by normalizing the energy measurement based on the path length.

66. The method of claim 65 or any other claim herein wherein determining path length associated with a trajectory of the corresponding particle through the detector comprises determining a trajectory of the corresponding particle through the detector.

67. The method of claim 66 or any other claim herein wherein determining the trajectory of the corresponding particle through the detector is based on the measured data obtained by the detector.

68. The method of any one of claims 66 to 67 or any other claim herein wherein determining the trajectory of the corresponding particle through the detector comprises determining two three-dimensional locations where the charged particle interacted with the detector.

69. The method of claim 68 or any other claim herein wherein determining the two three-dimensional locations where the charged particle interacted with the detector is based on the measured data obtained by the detector.

70. The method of any one of claims 63 to 69 or any other claim herein wherein obtaining the measured energy data comprises, for each detection event, adjusting the energy deposited by the corresponding particle per unit pathlength in the detector based on an attenuation parameter.

71. The method of clam 70 or any other claim herein wherein, for each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on the attenuation parameter comprises scaling (e.g. multiplying) the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

72. The method of any one of claims 70 to 71 or any other clam herein wherein, for each detection event, the attenuation parameter is based on an expected energy attenuation associated with interaction of the corresponding charged particle with the detector.

73. The method of claim 72 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a location where the corresponding charged particle interacts with the detector.

74. The method of claim 73 or any other claim herein comprising, for each detection event, determining the location where the corresponding charged particle interacts with the detector is based on the measured data obtained by the detector.

75. The method of any one of claims 73 to 74 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

76. The method of claim 75 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a distance between the location where the corresponding charged particle interacts with the detector and the location of the sensor.

77. The method of any one of claims 70 to 71 or any other clam herein wherein, for each detection event, the attenuation parameter is based on a distancebetween a location where the corresponding charged particle interacts with the detector and a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

78. The method of any one of claims 63 to 77 or any other claim herein wherein the first baseline environment has a high concentration (e.g. flux) of muon particles relative to a concentration (e.g. flux) of beta particles.

79. The method of any one of claims 63 to 78 or any other claim herein wherein the second baseline environment has a high concentration (e.g. flux) of beta particles relative to a concentration (e.g. flux) of muon particles.

80. The method of any one of claims 63 to 79 or any other claim herein wherein the muon detector used to obtain the measured distribution is of the same type of muon detector used to obtain the first and second baseline distributions.

81. The method of any one of claims 63 to 80 or any other claim herein wherein filtering the measured data obtained by the detector comprises determining a cut-off path-length-adjusted energy value.

82. The method of claim 81 or any other claim herein wherein filtering the measured data obtained by the detector comprises: keeping, in the noise- filtered measured data, detection events with path-length-adjusted energy values greater than the cut-off path-length-adjusted energy value; and rejecting, from the noise-filtered measured data, detection events with path- length-adjusted energy values less than the cut-off path-length-adjusted energy value.

83. The method of any one of claims 81 to 82 or any other claim herein wherein determining the cut-off path-length-adjusted energy value comprises minimizing a cost function parameterized by the plurality of distribution fitting parameters.

84. The method of claim 83 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector.

85. The method of any one of claims 83 to 84 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

86. The method of any one of claims 83 to 85 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the fitting of the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of a muon particle with the detector.

87. The method of any one of claims 83 to 86 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

88. The method of any one of claims 35 to 87 or any other claim herein wherein the plurality of distribution fitting parameters comprises, for each of the first and second based line distributions, one or more of: a peak location parameter, an amplitude scaling parameter and a variance scaling parameter.

89. The method of any one of claims 35 to 88 or any other claim herein comprising obtaining timing data associated with the measured data of each detectionevent, wherein determining the T-E discriminant value for each detection event is based on measured energy data, the measured trajectory data and the measured timing data corresponding to the detection event to thereby infer the T-E discriminant value for the detection event.

90. The method of claim 89 or any other claim herein wherein, for each detection event, the measured timing data comprises information that allows the determination of an estimated transit time of the charged particle through the muon detector.

91. The method of any one of claims 35 to 88 or any other claim herein comprising obtaining timing data associated with the measured data of each detection event and filtering the measured data based on the timing data, wherein the timing data for each detection event comprises information indicative of an estimated transit time of a charged particle through the muon detector.

92. The method of claim 91 or any other claim herein wherein filtering the measured data based on the timing data comprises, for each detection event, determining an expected time range based at least on the path length of the detection event and comparing the estimated transit time to the expected time range.

93. The method of claim 92 or any other claim herein wherein comparing the estimated transit time to the expected time range comprises excluding detection events with transit time outside the expected time range from the noise-filtered measured data and keeping detection events with transit time within the expected time range in the noise-filtered measured data.

94. The method of claim 91 or any other claim herein filtering the measured data based on the timing data comprises, for each detection event, calculating a particle speed based on the timing data and determining an acceptance range of an expected speed of muons based on the trajectory data and excluding detection events with calculated particle speed outside the acceptance range of the expected speed of muons and keeping detection events with calculatedparticle speed within the acceptance range of the expected speed of muons.

95. The method of any one of claims 91 to 94 or any other claim herein wherein the timing data for each detection event comprises at least a first time component of a first spatiotemporal point corresponding to a point of entry in the detection event and a second time component of a second spatiotemporal point corresponding to a point of exit in the detection event.

96. The method of claim 95 or any other claim herein wherein the estimated transit time of the charged particle for a given detection event is calculated as a difference between the first and second time components of the first and second spatiotemporal points.

97. An apparatus for filtering measured data obtained by a muon detector where the measured data comprises a plurality of detection events, each detection event associated with interaction of a corresponding charged particle with the muon detector, the apparatus comprising:an energy sensing system for determining, for each detection event, a measured energy deposited by the corresponding particle in the muon detector;a processor connected to the energy sensing system to receive, for each detection event, the measured energy, the processor configured to:determine, for each detection event, a measured trajectory representative of a path of the corresponding particle through the muon detector;determine, for each detection event, a T-E discriminant value based on the measured energy data and the measured trajectory data corresponding to the detection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality of detection events;fit the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein:the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment witha high concentration of muon particles relative to beta particles; the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; andfitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and,filter the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise-filtered measured data.

98. The apparatus of claim 98 or any other claim herein comprising any of the features, combinations of features and / or sub-combinations of features of any of claims 35 to 96.

99. A method for filtering noise from measured data obtained by a muon detector, the method comprising:obtaining measured energy data and measured trajectory data for a plurality of detection events, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the measured energy data is representative of energy deposited by the corresponding charged particle in the detector and the measured trajectory data is representative of a path of the corresponding charged particle through the detector;providing the measured energy data and the measured trajectory data as inputs into a machine learning algorithm, wherein the machine learning algorithm is trained to assign, as an output, a probability value to each detection event based on the corresponding measured energy data and measured trajectory data of the detection event, wherein the probability value reflects the probability of the corresponding detection event being a muon detection event; and,filtering or weighting the measured data obtained by the detector based at least on the probability values associated with the plurality of detection eventsto thereby obtain noise-filtered measured data.

100. A method for filtering noise from measured data obtained by a muon detector, the method comprising:obtaining measured energy data, measured trajectory data and measured timing data for a plurality of detection events, wherein each detection event is associated with interaction of a corresponding charged particle with the detector and, for each detection event, the measured energy data is representative of energy deposited by the corresponding charged particle in the detector, the measured trajectory data is representative of a path of the corresponding charged particle through the detector, and the measured timing data is indicative of an estimated transit time of the charged particle through the detector;determining, for each detection event, a T-E discriminant value based on the measured energy data, the measured trajectory data and the measured timing data corresponding to the detection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality of detection events;fitting the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein:the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; and fitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and,filtering the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise- filtered measured data.

101. The method of claim 100 or any other claim herein, wherein, for each detectionevent, an expected time rage is determined based at least in part on a path length of the path of the measured trajectory data and the expected time range is incorporated into the T-E discriminant value.

102. The method of any one of claims 100 to 101 or any other claim herein, wherein filtering the measured data obtained by the detector comprises determining a cut-off T-E discriminant value.

103. The method of claim 102 or any other claim herein wherein filtering the measured data obtained by the detector comprises: keeping, in the noise- filtered measured data, detection events with T-E discriminant values that are one of greater than or less than the cut-off T-E discriminant value; and rejecting, from the noise-filtered measured data, detection events with T-E discriminant values that are the other one of greater than or less than the cutoff T-E discriminant value.

104. The method of claim 102 or 103 or any other claim herein wherein determining the cut-off T-E discriminant value comprises minimizing a cost function.

105. The method of claim 104 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector.

106. The method of claim 104 or 105 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

107. The method of any one of claims 104 to 106 or any other claim herein whereinthe cost function comprises one or more terms that assign cost to rejecting, from the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of a muon particle with the detector.

108. The method of any one of claims 104 to 107 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting, from the noise-filtered measured data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

109. The method of any one of claims 100 to 108 or any other claim herein, wherein determining, for each detection event, the T-E discriminant value comprises applying a T-E discriminant determination model to the measured energy data, the measured trajectory data and the measured timing data corresponding to the detection event to thereby infer the T-E discriminant value for the detection event.

110. The method of claim 109 or any other claim herein wherein the T-E discriminant determination model comprises a machine-learning model comprising trainable parameters.111 The method of claim 110 or any other claim herein comprising training the machine-learning model, wherein training the machine-learning model comprises: initializing values for the trainable parameters; and performing a plurality of training iterations, each training iteration comprising:(i) determining, for each detection event in a set of labelled detection event training data, a T-E discriminant value based on current values for the trainable parameters of the T-E discriminant determination model to thereby obtain a corresponding distribution of T-E discriminant values;(ii) determining a T-E discriminant separation parameter for the corresponding distribution of T-E discriminant values, the T-E discriminantseparation parameter indicative of which detection events in the corresponding distribution of T-E discriminant values should be retained as being likely muon events and which detection events in the corresponding distribution of T-E discriminant values should be rejected as being unlikely to be muon events;(iii) applying the T-E discriminant separation parameter to the corresponding distribution of T-E discriminant values to thereby obtain a retained subset of detection events from within the set of labelled detection event data determined by the T-E discriminant determination model as being likely muon events and a rejection subset of detection events from within the set of labelled detection event data determined by the T-E discriminant determination model as being unlikely to be muon events;(iv) determining an evaluation score associated with the current values of the trainable parameters of the T-E discriminant determination model based on labels associated with the set of labelled detection event training data and at least one of: the retained subset of detection events and the rejection subset of detection events; and(v) modifying the values of the trainable parameters of the T-E discriminant determination model.

112. The method of claim 111 or any other claim herein wherein, for each iteration, the set of labelled detection event training data comprises: a subset of labelled muon detection training data corresponding to a plurality of detection events associated with a population of muon particles and a subset of labelled beta detection training data corresponding to a plurality of detection events associated with a population of beta particles.

113. The method of any one of claims 111 to 112 or any other claim herein wherein, for each iteration, the set of labelled detection event training data comprises, for each of a plurality of training detection events: trajectory data, energy data, timing data and a label indicating the training detection event to be either a muon event or a beta particle event.

114. The method of any one of claims 111 to 113 or any other claim herein wherein, for each iteration, the set of labelled detection event training data is differentfrom set of labelled detection event training data used in other iterations.

115. The method of any one of claims 111 to 114 or any other claim herein wherein, for each iteration, the set of labelled detection event training data is drawn from a larger collection of labelled detection event training data, wherein the larger collection of labelled detection event training data comprises, for each of a larger plurality of training detection events: trajectory data, energy data, timing data and a label indicating the event to be either a muon event or a beta particle event.

116. The method of claim 115 or any other claim herein wherein, for each iteration the set of labelled detection event training data is randomly drawn from the larger collection of labelled detection event training data.

117. The method of any one of claims 111 to 116 or any other claim herein wherein, for each iteration, determining the T-E discriminant separation parameter comprises determining optimizing a cost function to determine an optimal T-E discrimination separation parameter.

118. The method of claim 117 or any other claim herein wherein the cost function comprises one or more terms attributing cost to at least one of: retaining, in the retained subset, detection events from within the set of labelled detection event data labelled as beta particles or comprising beta particle labels; and rejecting, in the rejection subset, detection events from within the set of labelled detection event data labelled as muons or comprising muon labels.

119. The method of any one of claims 111 to 118 or any other claim herein wherein, for each iteration, determining the evaluation score comprises determining an efficiency of separation.

120. The method of claim 119 or any other claim herein wherein determining the efficiency of separation comprises at least one of:determining a ratio of a number of detection events in the retained subset that are labelled as muons or comprise muon labels to a total numberdetection events in the set of labelled detection evet training data that are labelled as muons or comprise muon labels; anddetermining a ratio of a number of detection events in the rejection subset that are labelled as beta particles or comprise beta particle labels to a total number detection events in the set of labelled detection evet training data that are labelled as beat particles or comprise beta particle labels.

121. The method of any one of claims 111 to 120 or any other claim herein wherein, for each iteration, determining the evaluation score comprises determining a purity of separation.

122. The method of claim 121 or any other claim herein wherein determining the purity of separation comprises at least one of:determining a ratio of a number of detection events in the retained subset that are labelled as muons or comprise muon labels to a total number of detection events in the retained subset; anddetermining a ratio of a number of detection events in the rejection subset that are labelled as beta particles or comprise beta particle labels to a total number of detection events in the rejection subset.

123. The method of any one of claims 111 to 122 or any other claim herein wherein, for each iteration, modifying the values of the trainable parameters is based at least in part on the determined evaluation score.

124. The method of any one of claims 111 to 123 or any other claim herein wherein, for each iteration, modifying the values of the trainable parameters comprises implementing back propagation.

125. The method of any one of claims 111 to 124 or any other claim herein wherein each iteration further comprises evaluating one or more training conclusion conditions and, if the one or more training conclusion conditions are met: ceasing training of the machine-learning model; and determining the machinelearning model with the current values of the trainable parameters to be the T- E discriminant determination model.

126. The method of claim 125 or any other claim herein wherein the one or more training conclusion conditions comprise at least one of: one or more of previously determined evaluation scores exceeding a threshold score; a probability of further improving the evaluation score with further training iterations is below a threshold probability; a change in a number of successive evaluation scores is below a threshold change; the evaluation score has not improved by more than a threshold amount over a threshold number of training iterations; and a number of training iterations exceeding a threshold number.

127. The method of any one of claims 100 to 109 or any other claim herein wherein, for each detection event, the T-E discriminant value comprises a path-length- and-attenuation-adjusted (PLAA) energy value.

128. The method of any one of claims 100 to 109 or any other claim herein wherein, for each detection event, the T-E discriminant value comprises a path-length- adjusted energy data representative of energy deposited by the corresponding per unit path length in the detector.

129. The method of claim 128 or any other claim herein wherein obtaining the measured energy data comprises, for each detection event, obtaining (e.g. measuring) an energy measurement representative of energy deposited by the corresponding particle in the detector.

130. The method of claim 129 or any other claim herein wherein obtaining the measured energy data comprises, for each detection event: determining a path length associated with a trajectory of the corresponding particle through the detector; and determining the path-length-adjusted energy data for the corresponding particle by normalizing the energy measurement based on the path length.

131. The method of claim 130 or any other claim herein wherein determining path length associated with a trajectory of the corresponding particle through the detector comprises determining a trajectory of the corresponding particlethrough the detector.

132. The method of claim 131 or any other claim herein wherein determining the trajectory of the corresponding particle through the detector is based on the measured data obtained by the detector.

133. The method of any one of claims 131 to 132 or any other claim herein wherein determining the trajectory of the corresponding particle through the detector comprises determining two three-dimensional locations where the charged particle interacted with the detector.

134. The method of claim 133 or any other claim herein wherein determining the two three-dimensional locations where the charged particle interacted with the detector is based on the measured data obtained by the detector.

135. The method of any one of claims 128 to 134 or any other claim herein wherein obtaining the measured energy data comprises, for each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

136. The method of clam 135 or any other claim herein wherein, for each detection event, adjusting the energy deposited by the corresponding particle per unit path length in the detector based on the attenuation parameter comprises scaling (e.g. multiplying) the energy deposited by the corresponding particle per unit path length in the detector based on an attenuation parameter.

137. The method of any one of claims 135 to 136 or any other clam herein wherein, for each detection event, the attenuation parameter is based on an expected energy attenuation associated with interaction of the corresponding charged particle with the detector.

138. The method of claim 137 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a location where the corresponding charged particle interacts with the detector.

139. The method of claim 138 or any other claim herein comprising, for each detection event, determining the location where the corresponding charged particle interacts with the detector is based on the measured data obtained by the detector.

140. The method of any one of claims 138 to 139 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

141. The method of claim 140 or any other claim herein wherein, for each detection event, the expected energy attenuation is based on a distance between the location where the corresponding charged particle interacts with the detector and the location of the sensor.

142. The method of any one of claims 135 to 136 or any other clam herein wherein, for each detection event, the attenuation parameter is based on a distance between a location where the corresponding charged particle interacts with the detector and a location of a sensor for obtaining a measurement representative of energy deposited by the corresponding charged particle in the detector.

143. The method of any one of claims 128 to 138 or any other claim herein wherein the first baseline environment has a high concentration (e.g. flux) of muon particles relative to a concentration (e.g. flux) of beta particles.

144. The method of any one of claims 128 to 143 or any other claim herein wherein the second baseline environment has a high concentration (e.g. flux) of beta particles relative to a concentration (e.g. flux) of muon particles.

145. The method of any one of claims 128 to 144 or any other claim herein wherein the muon detector used to obtain the measured distribution is of the same type of muon detector used to obtain the first and second baseline distributions.

146. The method of any one of claims 128 to 145 or any other claim herein wherein filtering the measured data obtained by the detector comprises determining a cut-off path-length-adjusted energy value.

147. The method of claim 146 or any other claim herein wherein filtering the measured data obtained by the detector comprises: keeping, in the noise- filtered measured data, detection events with path-length-adjusted energy values greater than the cut-off path-length-adjusted energy value; and rejecting, from the noise-filtered measured data, detection events with path- length-adjusted energy values less than the cut-off path-length-adjusted energy value.

148. The method of any one of claims 146 to 147 or any other claim herein wherein determining the cut-off path-length-adjusted energy value comprises minimizing a cost function parameterized by the plurality of distribution fitting parameters.

149. The method of claim 148 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events from within the plurality of detection events determined, by the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of beta particles with the detector.

150. The method of any one of claims 148 to 149 or any other claim herein wherein the cost function comprises one or more terms that assign cost to keeping, in the noise-filtered measured data, detection events within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of beta particles with the detector.

151. The method of any one of claims 148 to 150 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting,from the noise filtered measure data, detection events from within the plurality of detection events determined, by the fitting of the fitting of the measured distribution to the first and second baseline distributions, to be detection events associated with interaction of a muon particle with the detector.

152. The method of any one of claims 148 to 151 or any other claim herein wherein the cost function comprises one or more terms that assign cost to rejecting, from the noise filtered measure data, detection events from within the plurality of detection events determined, by the plurality of distribution fitting parameters, to be detection events associated with interaction of a muon particle with the detector.

153. The method of any one of claims 100 to 152 or any other claim herein wherein the plurality of distribution fitting parameters comprises, for each of the first and second based line distributions, one or more of: a peak location parameter, an amplitude scaling parameter and a variance scaling parameter.

154. An apparatus for filtering measured data obtained by a muon detector where the measured data comprises a plurality of detection events, each detection event associated with interaction of a corresponding charged particle with the muon detector, the apparatus comprising:an energy sensing system for determining, for each detection event, a measured energy deposited by the corresponding particle in the muon detector;a timing system for determining, for each detection event, timing data indicative of an estimated transit time of the charged particle through the muon detector;a processor connected to the energy sensing system and the timing system to receive, for each detection event, the measured energy and the measured timing data, the processor configured to:determine, for each detection event, a measured trajectory representative of a path of the corresponding particle through the muon detector;determine, for each detection event, a T-E discriminant value basedon the measured energy data, the measured trajectory data and the measured timing data corresponding to the detection event to thereby obtain a measured distribution of T-E discriminant values associated with the plurality of detection events;fit the measured distribution of T-E discriminant values to first and second baseline distributions of T-E discriminant values wherein: the first baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a first baseline environment with a high concentration of muon particles relative to beta particles; the second baseline distribution of T-E discriminant values is taken as an ansatz or obtained from a second baseline environment with a high concentration of beta particles relative to muon particles; andfitting the measured distribution to the first and second baseline distributions comprises determining a plurality of distribution fitting parameters; and,filter the measured data obtained by the detector based at least on the determined plurality of distribution fitting parameters to thereby obtain noise-filtered measured data.

155. The apparatus of claim 154 or any other claim herein comprising any of the features, combinations of features and / or sub-combinations of features of any of claims 100 to 153.

156. Apparatus having any new and inventive feature, combination of features, or sub-combination of features as described herein.

157. Methods having any new and inventive steps, acts, combination of steps and / or acts or sub-combination of steps and / or acts as described herein.

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